{VERSION 5 0 "IBM INTEL NT" "5.0" }
{USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 0 1 255 0 0 1 0 1 0 0 
1 0 0 0 0 1 }{CSTYLE "2D Math" -1 2 "Times" 0 1 0 0 0 0 0 0 2 0 0 0 0 
0 0 1 }{CSTYLE "2D Comment" 2 18 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }
{CSTYLE "2D Input" 2 19 "" 0 1 255 0 0 1 0 0 0 0 0 0 0 0 0 1 }{CSTYLE 
"2D Output" 2 20 "" 0 1 0 0 255 1 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 
256 "" 1 12 0 0 0 0 0 1 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 257 "" 1 12 0 
0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 258 "" 1 12 0 0 0 0 0 0 0 0 
0 0 0 0 0 1 }{CSTYLE "" -1 259 "" 1 12 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }
{CSTYLE "" -1 260 "" 1 14 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 
261 "" 0 14 0 0 0 0 0 1 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 262 "" 0 14 0 
0 0 0 0 1 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 263 "" 1 12 0 0 0 0 0 1 0 0 
0 0 0 0 0 1 }{CSTYLE "" -1 264 "" 0 14 0 0 0 0 0 1 0 0 0 0 0 0 0 1 }
{CSTYLE "" 19 265 "" 0 14 0 0 1 1 0 1 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 
266 "" 0 14 0 0 0 0 0 1 0 0 0 0 0 0 0 1 }{CSTYLE "" 19 267 "" 0 14 0 
0 1 1 0 1 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 268 "" 0 14 0 0 0 0 0 1 0 0 
0 0 0 0 0 1 }{CSTYLE "" -1 269 "" 0 1 0 0 1 1 0 1 0 0 0 0 0 0 0 1 }
{CSTYLE "" -1 270 "" 1 12 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 
271 "" 1 12 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 272 "" 0 14 0 
0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 273 "" 1 12 0 0 0 0 0 0 0 0 
0 0 0 0 0 1 }{CSTYLE "" -1 274 "" 1 12 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }
{CSTYLE "" -1 275 "" 1 12 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 
276 "" 1 12 0 0 0 0 0 2 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 277 "" 1 12 0 
0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 278 "" 0 14 0 0 1 1 0 0 0 0 
0 0 0 0 0 1 }{CSTYLE "" -1 279 "" 1 12 0 0 1 1 0 0 0 0 0 0 0 0 0 1 }
{CSTYLE "" -1 280 "" 1 12 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 
281 "" 1 12 0 0 1 1 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 282 "" 1 12 0 
0 1 1 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 283 "" 1 12 0 0 1 1 0 0 0 0 
0 0 0 0 0 1 }{CSTYLE "" -1 284 "" 1 12 0 0 1 1 0 0 0 0 0 0 0 0 0 1 }
{CSTYLE "" -1 285 "" 1 12 0 0 1 1 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 
286 "" 0 1 128 0 128 1 0 0 1 0 0 0 0 0 0 1 }{CSTYLE "" -1 287 "" 0 1 
128 0 128 1 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 288 "" 0 1 128 0 128 1 
0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 289 "" 0 1 128 0 128 1 0 0 0 0 0 0 
0 0 0 1 }{CSTYLE "" -1 290 "" 1 14 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }
{CSTYLE "" -1 291 "" 0 1 128 0 128 1 0 0 1 0 0 0 0 0 0 1 }{CSTYLE "" 
-1 292 "" 0 1 128 0 128 1 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 293 "" 0 
1 128 0 128 1 0 0 1 0 0 0 0 0 0 1 }{CSTYLE "" -1 294 "" 0 1 128 0 128 
1 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 295 "" 1 12 0 0 0 0 0 0 0 0 0 0 
0 0 0 1 }{CSTYLE "" -1 296 "" 1 12 0 0 0 0 0 1 0 0 0 0 0 0 0 1 }
{CSTYLE "" -1 297 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 
298 "" 0 1 128 0 128 1 0 0 1 0 0 0 0 0 0 1 }{CSTYLE "" -1 299 "" 0 1 
128 0 128 1 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 300 "" 0 14 0 0 0 0 0 
1 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 301 "" 1 14 0 0 0 0 0 1 0 0 0 0 0 0 
0 1 }{CSTYLE "" -1 302 "" 0 1 128 0 128 1 0 0 1 0 0 0 0 0 0 1 }
{CSTYLE "" -1 303 "" 0 1 128 0 128 1 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" 
-1 304 "" 1 14 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 305 "" 1 12 
0 0 0 0 0 1 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 306 "" 0 1 0 0 0 0 0 1 0 0 
0 0 0 0 0 1 }{CSTYLE "" -1 307 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 1 }
{CSTYLE "" -1 308 "" 1 14 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 
309 "" 0 1 128 0 128 1 0 0 1 0 0 0 0 0 0 1 }{CSTYLE "" -1 310 "" 0 1 
128 0 128 1 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 311 "" 1 14 0 0 0 0 0 
0 2 0 0 0 0 0 0 1 }{CSTYLE "" -1 312 "" 1 12 0 0 0 0 0 0 0 0 0 0 0 0 
0 1 }{CSTYLE "" -1 313 "" 1 12 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "
" -1 314 "" 0 1 128 0 128 1 0 0 1 0 0 0 0 0 0 1 }{CSTYLE "" -1 315 "" 
0 1 128 0 128 1 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 316 "" 1 12 0 0 0 
0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 317 "" 1 12 0 0 0 0 0 0 0 0 0 0 
0 0 0 1 }{CSTYLE "" -1 318 "" 1 14 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }
{CSTYLE "" -1 319 "" 0 1 128 0 128 1 0 0 1 0 0 0 0 0 0 1 }{CSTYLE "" 
-1 320 "" 0 1 128 0 128 1 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 321 "" 1 
12 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 322 "" 1 14 0 0 0 0 0 0 
0 0 0 0 0 0 0 1 }{CSTYLE "" -1 323 "" 1 12 0 0 0 0 0 0 0 0 0 0 0 0 0 
1 }{CSTYLE "" -1 324 "" 0 1 128 0 128 1 0 0 1 0 0 0 0 0 0 1 }{CSTYLE "
" -1 325 "" 0 1 128 0 128 1 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 326 "" 
0 1 0 0 1 1 0 1 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 327 "" 0 1 0 0 1 1 0 1 
0 0 0 0 0 0 0 1 }{CSTYLE "" -1 328 "" 0 1 0 0 1 1 0 1 0 0 0 0 0 0 0 1 
}{CSTYLE "" -1 329 "" 0 1 0 0 1 1 0 1 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 
330 "" 0 1 0 0 1 1 0 1 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 331 "" 0 1 0 0 
1 1 0 1 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 332 "" 0 1 0 0 1 1 0 1 0 0 0 0 
0 0 0 1 }{CSTYLE "" -1 333 "" 0 1 0 0 1 1 0 1 0 0 0 0 0 0 0 1 }
{CSTYLE "" -1 334 "" 0 1 128 0 128 1 0 0 1 0 0 0 0 0 0 1 }{CSTYLE "" 
-1 335 "" 0 1 128 0 128 1 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 336 "" 0 
1 128 0 128 1 0 0 1 0 0 0 0 0 0 1 }{CSTYLE "" -1 337 "" 0 1 128 0 128 
1 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 338 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 
0 0 1 }{CSTYLE "" -1 339 "" 1 12 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE 
"" -1 340 "" 0 1 128 0 128 1 0 0 1 0 0 0 0 0 0 1 }{CSTYLE "" -1 341 "
" 0 1 128 0 128 1 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 342 "" 1 12 0 0 
0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 343 "" 0 1 128 0 128 1 0 0 1 0 
0 0 0 0 0 1 }{CSTYLE "" -1 344 "" 0 1 128 0 128 1 0 0 0 0 0 0 0 0 0 1 
}{CSTYLE "" -1 345 "" 1 12 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 
346 "" 1 12 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" 18 347 "" 1 12 0 
0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" 18 348 "" 1 12 0 0 0 0 0 0 0 0 
0 0 0 0 0 0 }{CSTYLE "" -1 349 "" 1 12 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }
{CSTYLE "" 18 350 "" 1 12 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 
351 "" 1 12 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" 18 352 "" 1 12 0 
0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 353 "" 1 12 0 0 0 0 0 0 0 0 
0 0 0 0 0 1 }{CSTYLE "" 18 354 "" 1 12 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }
{CSTYLE "" -1 355 "" 1 12 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 
356 "" 1 12 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" 18 357 "" 1 12 0 
0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 358 "" 0 14 0 0 0 0 0 0 0 0 
0 0 0 0 0 1 }{CSTYLE "" -1 359 "" 0 14 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }
{CSTYLE "" -1 360 "" 0 14 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 
361 "" 1 12 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 362 "" 1 12 0 
0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" 18 363 "" 1 12 0 0 0 0 0 0 0 0 
0 0 0 0 0 0 }{CSTYLE "" -1 364 "" 1 12 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }
{CSTYLE "" 18 365 "" 1 12 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 
366 "" 1 12 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" 18 367 "" 1 12 0 
0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 368 "" 1 12 0 0 0 0 0 0 0 0 
0 0 0 0 0 0 }{CSTYLE "" -1 369 "" 1 12 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }
{CSTYLE "" -1 370 "" 1 12 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 
371 "" 1 12 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 372 "" 1 12 0 
0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" 18 373 "" 1 12 0 0 0 0 0 0 0 0 
0 0 0 0 0 0 }{CSTYLE "" -1 374 "" 0 1 128 0 128 1 0 0 1 0 0 0 0 0 0 1 
}{CSTYLE "" -1 375 "" 0 1 128 0 128 1 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" 
-1 376 "" 1 12 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 377 "" 1 12 
0 0 0 0 1 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 378 "" 1 12 0 0 0 0 0 0 0 
0 0 0 0 0 0 1 }{CSTYLE "" -1 379 "" 1 12 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }
{CSTYLE "" 18 380 "" 1 12 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 
381 "" 0 14 0 0 0 0 0 1 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 382 "" 1 12 0 
0 0 0 0 1 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 383 "" 1 12 0 0 0 0 0 1 0 0 
0 0 0 0 0 1 }{CSTYLE "" -1 384 "" 1 12 0 0 0 0 0 1 0 0 0 0 0 0 0 1 }
{CSTYLE "" -1 385 "" 1 12 0 0 0 0 0 1 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 
386 "" 1 12 0 0 0 0 0 1 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 387 "" 1 12 0 
0 0 0 0 1 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 388 "" 1 12 0 0 0 0 0 1 0 0 
0 0 0 0 0 1 }{CSTYLE "" -1 389 "" 1 12 0 0 1 1 0 1 0 0 0 0 0 0 0 1 }
{CSTYLE "" -1 390 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 
391 "" 1 12 0 0 1 1 0 1 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 392 "" 1 12 0 
0 0 0 0 1 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 393 "" 1 12 0 0 1 1 0 1 0 0 
0 0 0 0 0 1 }{CSTYLE "" -1 394 "" 0 1 128 0 128 1 0 0 1 0 0 0 0 0 0 1 
}{CSTYLE "" -1 395 "" 0 1 128 0 128 1 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" 
-1 396 "" 1 12 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 397 "" 1 14 
0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 398 "" 1 12 0 0 0 0 0 0 0 
0 0 0 0 0 0 1 }{CSTYLE "" 18 399 "" 1 12 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }
{CSTYLE "" -1 400 "" 1 12 0 0 0 0 0 1 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 
401 "" 0 14 0 0 0 0 0 1 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 402 "" 1 12 0 
0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 403 "" 0 1 0 0 1 1 0 1 0 0 0 
0 0 0 0 1 }{CSTYLE "" 19 404 "" 0 1 0 0 1 1 0 1 0 0 0 0 0 0 0 0 }
{CSTYLE "" 19 405 "" 0 1 0 0 1 1 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" 19 
406 "" 0 1 0 0 1 1 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" 19 407 "" 0 1 0 0 
1 1 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" 19 408 "" 0 1 0 0 1 1 0 1 0 0 0 0 
0 0 0 0 }{CSTYLE "" 19 409 "" 0 1 0 0 1 1 0 1 0 0 0 0 0 0 0 0 }
{CSTYLE "" 19 410 "" 0 1 0 0 1 1 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" 19 
411 "" 0 1 0 0 1 1 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" 18 412 "" 0 1 0 0 
1 1 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" 18 413 "" 0 1 0 0 1 1 0 1 0 0 0 0 
0 0 0 0 }{CSTYLE "" -1 414 "" 1 12 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }
{CSTYLE "" -1 415 "" 1 12 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" 18 
416 "" 1 12 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 417 "" 1 12 0 
0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" 18 418 "" 1 12 0 0 0 0 0 0 0 0 
0 0 0 0 0 0 }{CSTYLE "" -1 419 "" 1 12 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }
{CSTYLE "" 18 420 "" 1 12 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 
421 "" 1 12 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" 18 422 "" 1 12 0 
0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 423 "" 1 12 0 0 0 0 0 0 0 0 
0 0 0 0 0 0 }{CSTYLE "" 18 424 "" 1 12 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }
{CSTYLE "" -1 425 "" 1 12 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" 18 
426 "" 1 12 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 427 "" 1 12 0 
0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" 18 428 "" 1 12 0 0 0 0 0 0 0 0 
0 0 0 0 0 0 }{CSTYLE "" -1 429 "" 1 12 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }
{CSTYLE "" -1 430 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 
431 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 432 "" 1 12 0 0 
0 0 1 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 433 "" 1 12 0 0 0 0 0 1 0 0 0 
0 0 0 0 1 }{CSTYLE "" -1 434 "" 1 14 0 0 0 0 0 1 0 0 0 0 0 0 0 1 }
{CSTYLE "" -1 435 "" 1 14 0 0 0 0 1 1 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 
436 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 437 "" 0 1 0 0 
0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 438 "" 0 1 128 0 128 1 0 0 1 0 
0 0 0 0 0 1 }{CSTYLE "" -1 439 "" 0 1 128 0 128 1 0 0 0 0 0 0 0 0 0 1 
}{CSTYLE "" -1 440 "" 1 12 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" 18 
441 "" 1 12 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 442 "" 1 12 0 
0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" 18 443 "" 1 12 0 0 0 0 0 0 0 0 
0 0 0 0 0 0 }{CSTYLE "" -1 444 "" 1 12 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }
{CSTYLE "" -1 445 "" 1 14 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 
446 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 447 "" 0 1 0 0 
0 0 0 1 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 448 "" 1 12 0 0 0 0 0 1 0 0 0 
0 0 0 0 1 }{CSTYLE "" -1 449 "" 1 14 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }
{CSTYLE "" -1 450 "" 1 14 0 0 0 0 1 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 
451 "" 1 12 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 452 "" 0 1 128 
0 128 1 0 0 1 0 0 0 0 0 0 1 }{CSTYLE "" -1 453 "" 0 1 128 0 128 1 0 0 
0 0 0 0 0 0 0 1 }{CSTYLE "" -1 454 "" 1 12 0 0 0 0 0 0 0 0 0 0 0 0 0 
1 }{CSTYLE "" -1 455 "" 1 12 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" 
18 456 "" 1 12 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" 18 457 "" 1 12 
0 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 458 "" 1 14 0 0 0 0 0 0 0 
0 0 0 0 0 0 1 }{CSTYLE "" -1 459 "" 1 12 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }
{CSTYLE "" 18 460 "" 1 12 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 
461 "" 1 12 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" 18 462 "" 1 12 0 
0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 463 "" 1 12 0 0 0 0 0 0 0 0 
0 0 0 0 0 1 }{CSTYLE "" -1 464 "" 1 12 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }
{CSTYLE "" 18 465 "" 1 12 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 
466 "" 1 12 0 0 0 0 1 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 467 "" 1 12 0 
0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 468 "" 1 12 0 0 0 0 0 1 0 0 
0 0 0 0 0 1 }{CSTYLE "" -1 469 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 1 }
{CSTYLE "" -1 470 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 
471 "" 1 14 0 0 0 0 0 1 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 472 "" 1 14 0 
0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" 18 473 "" 1 12 0 0 0 0 0 0 0 0 
0 0 0 0 0 0 }{CSTYLE "" -1 474 "" 1 12 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }
{CSTYLE "" -1 475 "" 1 14 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 
476 "" 0 14 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 477 "" 1 14 0 
0 0 0 0 1 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 478 "" 1 12 0 0 0 0 0 0 0 0 
0 0 0 0 0 1 }{CSTYLE "" -1 479 "" 1 12 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }
{CSTYLE "" 18 480 "" 1 12 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" 18 
481 "" 1 12 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 482 "" 1 12 0 
0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" 18 483 "" 1 12 0 0 0 0 0 0 0 0 
0 0 0 0 0 0 }{CSTYLE "" -1 484 "" 1 12 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }
{CSTYLE "" 18 485 "" 1 12 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 
486 "" 1 12 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" 18 487 "" 1 12 0 
0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 488 "" 1 12 0 0 0 0 0 0 0 0 
0 0 0 0 0 1 }{CSTYLE "" -1 489 "" 1 12 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }
{CSTYLE "" -1 490 "" 1 12 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 
491 "" 1 12 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 492 "" 1 12 0 
0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" 18 493 "" 1 12 0 0 0 0 0 0 0 0 
0 0 0 0 0 0 }{CSTYLE "" 18 494 "" 1 12 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }
{CSTYLE "" 18 495 "" 1 12 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" 18 
496 "" 1 12 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" 18 497 "" 1 12 0 
0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 498 "" 1 12 0 0 0 0 0 0 0 0 
0 0 0 0 0 1 }{CSTYLE "" -1 499 "" 1 12 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }
{CSTYLE "" -1 500 "" 1 12 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 
501 "" 1 12 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 502 "" 1 12 0 
0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" 18 503 "" 1 12 0 0 0 0 0 0 0 0 
0 0 0 0 0 0 }{CSTYLE "" 18 504 "" 1 12 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }
{CSTYLE "" 18 505 "" 1 12 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" 18 
506 "" 1 12 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 507 "" 1 12 0 
0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 508 "" 1 12 0 0 0 0 0 0 0 0 
0 0 0 0 0 1 }{CSTYLE "" -1 509 "" 1 12 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }
{CSTYLE "" -1 510 "" 1 12 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 
511 "" 1 12 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 512 "" 1 12 0 
0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 513 "" 1 12 0 0 0 0 0 0 0 0 
0 0 0 0 0 1 }{CSTYLE "" -1 514 "" 1 12 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }
{CSTYLE "" -1 515 "" 1 12 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 
516 "" 1 12 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 517 "" 1 12 0 
0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 518 "" 1 12 0 0 0 0 0 0 0 0 
0 0 0 0 0 1 }{CSTYLE "" -1 519 "" 1 12 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }
{CSTYLE "" 18 520 "" 1 12 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 
521 "" 1 12 0 0 1 1 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 522 "" 1 12 0 
0 1 1 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 523 "" 1 12 0 0 1 1 0 0 0 0 
0 0 0 0 0 1 }{CSTYLE "" -1 524 "" 1 12 0 0 1 1 0 0 0 0 0 0 0 0 0 1 }
{CSTYLE "" -1 525 "" 1 12 0 0 1 1 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" 19 
526 "" 0 1 0 0 1 1 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" 19 527 "" 0 1 0 0 
1 1 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" 19 528 "" 0 1 0 0 1 1 0 0 0 0 0 0 
0 0 0 0 }{CSTYLE "" 19 529 "" 0 1 0 0 1 1 0 0 0 0 0 0 0 0 0 0 }
{CSTYLE "" 18 530 "" 0 1 0 0 1 1 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" 19 
531 "" 0 1 0 0 1 1 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" 19 532 "" 0 1 0 0 
1 1 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" 18 533 "" 0 1 0 0 1 1 0 0 0 0 0 0 
0 0 0 0 }{CSTYLE "" 18 534 "" 0 1 0 0 1 1 0 0 0 0 0 0 0 0 0 0 }
{CSTYLE "" 19 535 "" 0 1 0 0 1 1 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 
536 "" 1 12 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" 18 537 "" 1 12 0 
0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 538 "" 1 12 0 0 0 0 0 0 0 0 
0 0 0 0 0 1 }{CSTYLE "" 18 539 "" 1 12 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }
{CSTYLE "" -1 540 "" 1 12 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 
541 "" 1 12 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 542 "" 0 1 0 0 
0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 543 "" 1 12 0 0 0 0 0 1 0 0 0 
0 0 0 0 1 }{CSTYLE "" -1 544 "" 1 12 0 0 0 0 1 0 0 0 0 0 0 0 0 0 }
{CSTYLE "" -1 545 "" 1 14 0 0 0 0 0 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 
546 "" 1 12 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" 18 547 "" 1 12 0 
0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 548 "" 1 14 0 0 0 0 0 0 0 0 
0 0 0 0 0 0 }{CSTYLE "" -1 549 "" 1 14 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }
{CSTYLE "" -1 550 "" 1 12 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 
551 "" 1 12 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 552 "" 1 12 0 
0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" 18 553 "" 1 12 0 0 0 0 0 0 0 0 
0 0 0 0 0 0 }{CSTYLE "" 18 554 "" 1 12 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }
{CSTYLE "" -1 555 "" 1 12 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 
556 "" 1 14 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 557 "" 1 12 0 
0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 558 "" 1 12 0 0 0 0 0 1 0 0 
0 0 0 0 0 0 }{CSTYLE "" -1 559 "" 1 12 0 0 0 0 0 1 0 0 0 0 0 0 0 0 }
{CSTYLE "" -1 567 "" 0 1 128 0 128 1 0 0 1 0 0 0 0 0 0 1 }{CSTYLE "" 
-1 568 "" 0 1 128 0 128 1 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 569 "" 0 
1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" 18 570 "" 0 1 0 0 0 0 0 1 0 
0 0 0 0 0 0 0 }{CSTYLE "" -1 571 "" 1 12 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }
{CSTYLE "" -1 572 "" 1 12 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" 18 
573 "" 1 12 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 574 "" 0 1 0 0 
0 0 0 1 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 575 "" 1 12 0 0 0 0 0 1 0 0 0 
0 0 0 0 1 }{CSTYLE "" -1 576 "" 1 14 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }
{CSTYLE "" -1 577 "" 1 14 0 0 0 0 1 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 
578 "" 1 12 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 579 "" 1 12 0 
0 0 0 0 1 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 580 "" 1 12 0 0 0 0 0 0 0 0 
0 0 0 0 0 1 }{CSTYLE "" -1 581 "" 1 12 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }
{CSTYLE "" 18 582 "" 1 12 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 
583 "" 1 12 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 584 "" 1 12 0 
0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 585 "" 1 12 0 0 0 0 0 0 0 0 
0 0 0 0 0 1 }{CSTYLE "" 18 586 "" 1 12 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }
{CSTYLE "" 18 587 "" 1 12 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" 18 
588 "" 1 12 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" 18 589 "" 1 12 0 
0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 590 "" 1 14 0 0 0 0 0 0 0 0 
0 0 0 0 0 1 }{CSTYLE "" -1 591 "" 1 18 128 0 128 1 0 1 1 0 0 0 0 0 0 
1 }{CSTYLE "" -1 592 "" 1 18 128 0 128 1 0 1 0 0 0 0 0 0 0 1 }{CSTYLE 
"" -1 593 "" 1 12 0 0 0 0 0 1 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 594 "" 0 
14 0 0 0 0 0 1 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 595 "" 1 14 0 0 0 0 0 0 
0 0 0 0 0 0 0 1 }{CSTYLE "" -1 596 "" 1 12 0 0 0 0 0 0 0 0 0 0 0 0 0 
0 }{CSTYLE "" 18 597 "" 1 12 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" 
-1 598 "" 1 12 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" 18 599 "" 1 12 
0 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 600 "" 1 12 0 0 0 0 0 0 0 
0 0 0 0 0 0 0 }{CSTYLE "" 18 601 "" 1 12 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }
{CSTYLE "" -1 602 "" 1 12 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 
603 "" 0 1 128 0 128 1 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 604 "" 1 12 
0 0 0 0 0 1 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 605 "" 0 14 0 0 0 0 0 1 0 
0 0 0 0 0 0 1 }{CSTYLE "" -1 606 "" 1 14 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }
{CSTYLE "" -1 607 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 
608 "" 1 12 0 0 0 0 0 1 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 609 "" 1 14 0 
0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 610 "" 1 14 0 0 0 0 1 0 0 0 
0 0 0 0 0 1 }{CSTYLE "" -1 611 "" 1 12 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }
{CSTYLE "" -1 612 "" 1 12 0 0 0 0 0 1 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 
613 "" 1 12 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 615 "" 0 1 128 
0 128 1 0 0 1 0 0 0 0 0 0 1 }{PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 
"Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }1 1 0 0 0 0 1 0 1 0 2 2 0 1 
}{PSTYLE "Heading 1" -1 3 1 {CSTYLE "" -1 -1 "Times" 1 18 0 0 0 1 2 1 
2 2 2 2 1 1 1 1 }1 1 0 0 8 4 1 0 1 0 2 2 0 1 }{PSTYLE "Maple Output" 
-1 11 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }3 
3 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Maple Plot" -1 13 1 {CSTYLE "" -1 
-1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }3 1 0 0 0 0 1 0 1 0 2 2 
0 1 }{PSTYLE "Title" -1 18 1 {CSTYLE "" -1 -1 "Times" 1 18 0 0 0 1 2 
1 1 2 2 2 1 1 1 1 }3 1 0 0 12 12 1 0 1 0 2 2 19 1 }{PSTYLE "Normal" 
-1 256 1 {CSTYLE "" -1 -1 "Times" 1 18 0 0 0 1 2 1 2 2 2 2 1 1 1 1 }1 
1 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Heading 1" -1 257 1 {CSTYLE "" -1 
-1 "Times" 1 14 0 0 0 1 2 1 2 2 2 2 1 1 1 1 }1 1 0 0 8 4 1 0 1 0 2 2 
0 1 }{PSTYLE "Normal" -1 258 1 {CSTYLE "" -1 -1 "Times" 1 14 0 0 0 1 
2 1 2 2 2 2 1 1 1 1 }1 1 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Normal" -1 
259 1 {CSTYLE "" -1 -1 "Times" 1 14 0 0 0 1 2 1 1 2 2 2 1 1 1 1 }1 1 
0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Heading 1" -1 260 1 {CSTYLE "" -1 
-1 "Times" 1 12 0 0 0 1 2 1 2 2 2 2 1 1 1 1 }1 1 0 0 8 4 1 0 1 0 2 2 
0 1 }{PSTYLE "Normal" -1 261 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 
2 1 2 2 2 2 1 1 1 1 }1 1 0 0 0 0 1 0 1 0 2 2 0 1 }}
{SECT 0 {EXCHG {PARA 18 "" 0 "" {TEXT 311 36 "       Math 132  \n Fall
 2007  Exam I" }}{PARA 0 "" 0 "" {TEXT 256 3 "   " }}}{SECT 0 {PARA 3 
"" 0 "" {TEXT 545 8 "Notation" }{TEXT 555 62 ":     D(f)(x)    means: \+
 \"the derivative of  f  evaluated at  " }{TEXT 544 1 "x" }{TEXT 546 
20 ".\"   For example, if" }{TEXT 549 3 "   " }{XPPEDIT 547 0 "f(x) = \+
x^3;" "6#/-%\"fG6#%\"xG*$F'\"\"$" }{TEXT 548 2 ", " }{TEXT 552 6 "then
  " }{XPPEDIT 553 0 "D(f)(x) = 3*x^2;" "6#/--%\"DG6#%\"fG6#%\"xG*&\"\"
$\"\"\"*$F*\"\"#F-" }{TEXT 550 7 "  and  " }{XPPEDIT 554 0 "D(f)(5) = \+
75;" "6#/--%\"DG6#%\"fG6#\"\"&\"#v" }{TEXT 551 2 ". " }}}{SECT 0 
{PARA 3 "" 0 "" {TEXT 258 1 "1" }{TEXT 264 2 ". " }{TEXT 312 16 " A Ri
emann sum  " }{XPPEDIT 350 0 "sum(f(s[j])*Delta*x,j = 1 .. N);" "6#-%$
sumG6$*(-%\"fG6#&%\"sG6#%\"jG\"\"\"%&DeltaGF.%\"xGF./F-;F.%\"NG" }
{TEXT 349 19 "   for a function  " }{XPPEDIT 347 0 "f;" "6#%\"fG" }
{TEXT 345 18 "  on an interval  " }{XPPEDIT 348 0 "[a, b];" "6#7$%\"aG
%\"bG" }{TEXT 346 19 "  is said to be an " }{TEXT 377 17 "upper Rieman
n sum" }{TEXT 378 16 " if, for each   " }{XPPEDIT 352 0 "j;" "6#%\"jG
" }{TEXT 351 15 ",  \nthe point  " }{XPPEDIT 354 0 "s[j];" "6#&%\"sG6#
%\"jG" }{TEXT 353 10 "  in the  " }{XPPEDIT 473 0 "j;" "6#%\"jG" }
{XPPEDIT 18 0 "` `^th;" "6#)%\"~G%#thG" }{TEXT 474 34 "   subinterval \+
is chosen so that  " }{XPPEDIT 256 0 "f(s[j]);" "6#-%\"fG6#&%\"sG6#%\"
jG" }{TEXT 355 27 "  is the maximum value of  " }{XPPEDIT 537 0 "f(x);
" "6#-%\"fG6#%\"xG" }{TEXT 536 6 " for  " }{XPPEDIT 539 0 "x;" "6#%\"x
G" }{TEXT 538 10 "  in the  " }{XPPEDIT 257 0 "j;" "6#%\"jG" }
{XPPEDIT 18 0 "` `^th;" "6#)%\"~G%#thG" }{TEXT 540 51 "   subinterval.
   \nUsing the uniform partition of  " }{XPPEDIT 258 0 "[a, b] = [0, 6
];" "6#/7$%\"aG%\"bG7$\"\"!\"\"'" }{TEXT 541 72 " into 3 subintervals,
 calculate the upper Riemann sum for the function  " }{XPPEDIT 357 0 "
f;" "6#%\"fG" }{TEXT 356 23 "  whose graph is given." }}{PARA 0 "" 0 "
" {TEXT -1 0 "" }}{PARA 261 "" 0 "" {TEXT -1 95 "a) 13           b)   \+
14            c)  15            d)   16           e)  17  \nf)  18    \+
     " }{TEXT 313 65 "  g)  19            h)  20             i)   21  \+
          j)  22 " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" 
{TEXT -1 0 "" }}{PARA 13 "" 1 "" {GLPLOT2D 741 302 302 {PLOTDATA 2 "6/
-%'CURVESG6%7(7$$\"\"!F)$\"\"\"F)7$F*$\"\"%F)7$$\"\"#F)F07$F-$\"\"$F)7
$$\"\"&F)F(7$$\"\"'F)F0-%'COLOURG6&%$RGBGF(F(F(-%*THICKNESSG6#F4-F$6$7
SF'7$$\"3%*******\\#HyI\"!#=F*7$$\"33++]([kdW#FHF*7$$\"3++++v;\\DPFHF*
7$$\"3W+++D<q8]FHF*7$$\"3o****\\P\"*y&H'FHF*7$$\"3e****\\(G[W[(FHF*7$$
\"3i****\\()fB:()FHF*7$$\"39++](Q=\"))**FHF*7$$\"3(****\\P'=pD6!#<F*7$
$\"33+++lN?c7F[oF*7$$\"3-++]U$e6P\"F[oF*7$$\"36+++&>q0]\"F[oF*7$$\"3'*
*****\\U80j\"F[oF*7$$\"35+++0ytb<F[oF*7$$\"3)****\\(QNXp=F[oF*7$$\"3.+
++XDn/?F[oF*7$$\"3.+++!y?#>@F[oF*7$$\"3'****\\(3wY_AF[oF*7$$\"3#)*****
*HOTqBF[oF*7$$\"37++v3\">)*\\#F[oF*7$$\"3:++DEP/BEF[oF*7$$\"3=++](o:;v
#F[oF*7$$\"3=++v$)[opGF[oF*7$$\"3%*****\\i%Qq*HF[oF*7$$\"3&****\\(QIKH
JF[oF*7$$\"3#****\\7:xWC$F[oF*7$$\"37++]Zn%)oLF[oF*7$$\"3y******4FL(\\
$F[oF*7$$\"3#)****\\d6.BOF[oF*7$$\"3(****\\(o3lWPF[oF*7$$\"3!*****\\A)
)ozQF[oF*7$$\"3e******Hk-,SF[oF*7$$\"36+++D-eITF[oF*7$$\"3u***\\(=_(zC
%F[oF*7$$\"3M+++b*=jP%F[oF*7$$\"3g***\\(3/3(\\%F[oF*7$$\"33++vB4JBYF[o
F*7$$\"3u*****\\KCnu%F[oF*7$$\"3s***\\(=n#f([F[oF*7$$\"3P+++!)RO+]F[oF
*7$$\"30++]_!>w7&F[oF*7$$\"3O++v)Q?QD&F[oF*7$$\"3G+++5jyp`F[oF*7$$\"3<
++]Ujp-bF[oF*7$$\"3++++gEd@cF[oF*7$$\"39++v3'>$[dF[oF*7$$\"37++D6EjpeF
[oF*7$F9F*-%&COLORG6&F>$\"\")!\"\"FbvFbv-F$6$7S7$F(F07$FFF07$FJF07$FMF
07$FPF07$FSF07$FVF07$FYF07$FfnF07$FinF07$F]oF07$F`oF07$FcoF07$FfoF07$F
ioF07$F\\pF07$F_pF07$FbpF07$FepF07$FhpF07$F[qF07$F^qF07$FaqF07$FdqF07$
FgqF07$FjqF07$F]rF07$F`rF07$FcrF07$FfrF07$FirF07$F\\sF07$F_sF07$FbsF07
$FesF07$FhsF07$F[tF07$F^tF07$FatF07$FdtF07$FgtF07$FjtF07$F]uF07$F`uF07
$FcuF07$FfuF07$FiuF07$F\\vF0F8F_v-F$6$7S7$F(F37$FFF37$FJF37$FMF37$FPF3
7$FSF37$FVF37$FYF37$FfnF37$FinF37$F]oF37$F`oF37$FcoF37$FfoF37$FioF37$F
\\pF37$F_pF37$FbpF37$FepF37$FhpF37$F[qF37$F^qF37$FaqF37$FdqF37$FgqF37$
FjqF37$F]rF37$F`rF37$FcrF37$FfrF37$FirF37$F\\sF37$F_sF37$FbsF37$FesF37
$FhsF37$F[tF37$F^tF37$FatF37$FdtF37$FgtF37$FjtF37$F]uF37$F`uF37$FcuF37
$FfuF37$FiuF37$F\\vF37$F9F3F_v-F$6$7S7$F(F-7$FFF-7$FJF-7$FMF-7$FPF-7$F
SF-7$FVF-7$FYF-7$FfnF-7$FinF-7$F]oF-7$F`oF-7$FcoF-7$FfoF-7$FioF-7$F\\p
F-7$F_pF-7$FbpF-7$FepF-7$FhpF-7$F[qF-7$F^qF-7$FaqF-7$FdqF-7$FgqF-7$Fjq
F-7$F]rF-7$F`rF-7$FcrF-7$FfrF-7$FirF-7$F\\sF-7$F_sF-7$FbsF-7$FesF-7$Fh
sF-7$F[tF-7$F^tF-7$FatF-7$FdtF-7$FgtF-7$FjtF-7$F]uF-7$F`uF-7$FcuF-7$Ff
uF-7$FiuF-7$F\\vF-7$F9F-F_v-F$6$7S7$F*F(7$F*$\"3Hmmmm;')=()!#>7$F*$\"3
RLLLe'40j\"FH7$F*$\"3mmmm;6m$[#FH7$F*$\"3fmmm;yYULFH7$F*$\"3%HLL$eF>(>
%FH7$F*$\"3Qmmm\">K'*)\\FH7$F*$\"3P*****\\Kd,\"eFH7$F*$\"3-mmm\"fX(emF
H7$F*$\"3.*****\\U7Y](FH7$F*$\"3'QLLLV!pu$)FH7$F*$\"3xmmm;c0T\"*FH7$F*
$\"3#*******H,Q+5F[o7$F*$\"3)*******\\*3q3\"F[o7$F*$\"3)*******p=\\q6F
[o7$F*$\"3mmm;fBIY7F[o7$F*$\"3GLLLj$[kL\"F[o7$F*$\"3?LLL`Q\"GT\"F[o7$F
*$\"3!*****\\s]k,:F[o7$F*$\"39LLL`dF!e\"F[o7$F*$\"33++]sgam;F[o7$F*$\"
3/++]<ep[<F[o7$F*$\"3QLLLe/TM=F[o7$F*$\"3JLL$eDBJ\">F[o7$F*$\"3immmTc-
)*>F[o7$F*$\"3Mmm;f`@'3#F[o7$F*$\"3y****\\nZ)H;#F[o7$F*$\"3YmmmJy*eC#F
[o7$F*$\"3')******R^bJBF[o7$F*$\"3f*****\\5a`T#F[o7$F*$\"3o****\\7RV'
\\#F[o7$F*$\"3k*****\\@fke#F[o7$F*$\"3/LLL`4NnEF[o7$F*$\"3#*******\\,s
`FF[o7$F*$\"3[mm;zM)>$GF[o7$F*$\"3$*******pfa<HF[o7$F*$\"3#HLLeg`!)*HF
[o7$F*$\"3w****\\#G2A3$F[o7$F*$\"3;LLL$)G[kJF[o7$F*$\"3#)****\\7yh]KF[
o7$F*$\"3xmmm')fdLLF[o7$F*$\"3bmmm,FT=MF[o7$F*$\"3FLL$e#pa-NF[o7$F*$\"
3!*******Rv&)zNF[o7$F*$\"3ILLLGUYoOF[o7$F*$\"3_mmm1^rZPF[o7$F*$\"34++]
sI@KQF[o7$F*$\"34++]2%)38RF[oF,F_v-F$6$7S7$F0F(7$F0Fe`l7$F0Fi`l7$F0F\\
al7$F0F_al7$F0Fbal7$F0Feal7$F0Fhal7$F0F[bl7$F0F^bl7$F0Fabl7$F0Fdbl7$F0
Fgbl7$F0Fjbl7$F0F]cl7$F0F`cl7$F0Fccl7$F0Ffcl7$F0Ficl7$F0F\\dl7$F0F_dl7
$F0Fbdl7$F0Fedl7$F0Fhdl7$F0F[el7$F0F^el7$F0Fael7$F0Fdel7$F0Fgel7$F0Fje
l7$F0F]fl7$F0F`fl7$F0Fcfl7$F0Fffl7$F0Fifl7$F0F\\gl7$F0F_gl7$F0Fbgl7$F0
Fegl7$F0Fhgl7$F0F[hl7$F0F^hl7$F0Fahl7$F0Fdhl7$F0Fghl7$F0Fjhl7$F0F]il7$
F0F`il7$F0F-F_v-F$6$7S7$F3F(7$F3Fe`l7$F3Fi`l7$F3F\\al7$F3F_al7$F3Fbal7
$F3Feal7$F3Fhal7$F3F[bl7$F3F^bl7$F3Fabl7$F3Fdbl7$F3Fgbl7$F3Fjbl7$F3F]c
l7$F3F`cl7$F3Fccl7$F3Ffcl7$F3Ficl7$F3F\\dl7$F3F_dl7$F3Fbdl7$F3Fedl7$F3
Fhdl7$F3F[el7$F3F^el7$F3Fael7$F3Fdel7$F3Fgel7$F3Fjel7$F3F]fl7$F3F`fl7$
F3Fcfl7$F3Fffl7$F3Fifl7$F3F\\gl7$F3F_gl7$F3Fbgl7$F3Fegl7$F3Fhgl7$F3F[h
l7$F3F^hl7$F3Fahl7$F3Fdhl7$F3Fghl7$F3Fjhl7$F3F]il7$F3F`il7$F3F-F_v-F$6
$7S7$F-F(7$F-Fe`l7$F-Fi`l7$F-F\\al7$F-F_al7$F-Fbal7$F-Feal7$F-Fhal7$F-
F[bl7$F-F^bl7$F-Fabl7$F-Fdbl7$F-Fgbl7$F-Fjbl7$F-F]cl7$F-F`cl7$F-Fccl7$
F-Ffcl7$F-Ficl7$F-F\\dl7$F-F_dl7$F-Fbdl7$F-Fedl7$F-Fhdl7$F-F[el7$F-F^e
l7$F-Fael7$F-Fdel7$F-Fgel7$F-Fjel7$F-F]fl7$F-F`fl7$F-Fcfl7$F-Fffl7$F-F
ifl7$F-F\\gl7$F-F_gl7$F-Fbgl7$F-Fegl7$F-Fhgl7$F-F[hl7$F-F^hl7$F-Fahl7$
F-Fdhl7$F-Fghl7$F-Fjhl7$F-F]il7$F-F`il7$F-F-F_v-F$6$7SF57$F6Fe`l7$F6Fi
`l7$F6F\\al7$F6F_al7$F6Fbal7$F6Feal7$F6Fhal7$F6F[bl7$F6F^bl7$F6Fabl7$F
6Fdbl7$F6Fgbl7$F6Fjbl7$F6F]cl7$F6F`cl7$F6Fccl7$F6Ffcl7$F6Ficl7$F6F\\dl
7$F6F_dl7$F6Fbdl7$F6Fedl7$F6Fhdl7$F6F[el7$F6F^el7$F6Fael7$F6Fdel7$F6Fg
el7$F6Fjel7$F6F]fl7$F6F`fl7$F6Fcfl7$F6Fffl7$F6Fifl7$F6F\\gl7$F6F_gl7$F
6Fbgl7$F6Fegl7$F6Fhgl7$F6F[hl7$F6F^hl7$F6Fahl7$F6Fdhl7$F6Fghl7$F6Fjhl7
$F6F]il7$F6F`il7$F6F-F_v-F$6$7S7$F9F(7$F9Fe`l7$F9Fi`l7$F9F\\al7$F9F_al
7$F9Fbal7$F9Feal7$F9Fhal7$F9F[bl7$F9F^bl7$F9Fabl7$F9Fdbl7$F9Fgbl7$F9Fj
bl7$F9F]cl7$F9F`cl7$F9Fccl7$F9Ffcl7$F9Ficl7$F9F\\dl7$F9F_dl7$F9Fbdl7$F
9Fedl7$F9Fhdl7$F9F[el7$F9F^el7$F9Fael7$F9Fdel7$F9Fgel7$F9Fjel7$F9F]fl7
$F9F`fl7$F9Fcfl7$F9Fffl7$F9Fifl7$F9F\\gl7$F9F_gl7$F9Fbgl7$F9Fegl7$F9Fh
gl7$F9F[hl7$F9F^hl7$F9Fahl7$F9Fdhl7$F9Fghl7$F9Fjhl7$F9F]il7$F9F`ilF_`l
F_v-%+AXESLABELSG6%Q!6\"Fgim-%%FONTG6#%(DEFAULTG-%%VIEWG6$;F(F9F\\jm" 
1 2 0 1 10 0 2 9 1 4 2 1.000000 45.000000 45.000000 0 0 "Curve 1" "Cur
ve 2" "Curve 3" "Curve 4" "Curve 5" "Curve 6" "Curve 7" "Curve 8" "Cur
ve 9" "Curve 10" "Curve 11" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 
0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 3 "" 
0 "" {TEXT 314 8 "Solution" }{TEXT 315 6 ": (h)\n" }}{PARA 0 "" 0 "" 
{TEXT -1 4 "    " }}{PARA 13 "" 1 "" {GLPLOT2D 729 296 296 {PLOTDATA 
2 "62-%'CURVESG6%7(7$$\"\"!F)$\"\"\"F)7$F*$\"\"%F)7$$\"\"#F)F07$F-$\"
\"$F)7$$\"\"&F)F(7$$\"\"'F)F0-%'COLOURG6&%$RGBGF(F(F(-%*THICKNESSG6#F4
-F$6$7SF'7$$\"3%*******\\#HyI\"!#=F*7$$\"33++]([kdW#FHF*7$$\"3++++v;\\
DPFHF*7$$\"3W+++D<q8]FHF*7$$\"3o****\\P\"*y&H'FHF*7$$\"3e****\\(G[W[(F
HF*7$$\"3i****\\()fB:()FHF*7$$\"39++](Q=\"))**FHF*7$$\"3(****\\P'=pD6!
#<F*7$$\"33+++lN?c7F[oF*7$$\"3-++]U$e6P\"F[oF*7$$\"36+++&>q0]\"F[oF*7$
$\"3'******\\U80j\"F[oF*7$$\"35+++0ytb<F[oF*7$$\"3)****\\(QNXp=F[oF*7$
$\"3.+++XDn/?F[oF*7$$\"3.+++!y?#>@F[oF*7$$\"3'****\\(3wY_AF[oF*7$$\"3#
)******HOTqBF[oF*7$$\"37++v3\">)*\\#F[oF*7$$\"3:++DEP/BEF[oF*7$$\"3=++
](o:;v#F[oF*7$$\"3=++v$)[opGF[oF*7$$\"3%*****\\i%Qq*HF[oF*7$$\"3&****
\\(QIKHJF[oF*7$$\"3#****\\7:xWC$F[oF*7$$\"37++]Zn%)oLF[oF*7$$\"3y*****
*4FL(\\$F[oF*7$$\"3#)****\\d6.BOF[oF*7$$\"3(****\\(o3lWPF[oF*7$$\"3!**
***\\A))ozQF[oF*7$$\"3e******Hk-,SF[oF*7$$\"36+++D-eITF[oF*7$$\"3u***
\\(=_(zC%F[oF*7$$\"3M+++b*=jP%F[oF*7$$\"3g***\\(3/3(\\%F[oF*7$$\"33++v
B4JBYF[oF*7$$\"3u*****\\KCnu%F[oF*7$$\"3s***\\(=n#f([F[oF*7$$\"3P+++!)
RO+]F[oF*7$$\"30++]_!>w7&F[oF*7$$\"3O++v)Q?QD&F[oF*7$$\"3G+++5jyp`F[oF
*7$$\"3<++]Ujp-bF[oF*7$$\"3++++gEd@cF[oF*7$$\"39++v3'>$[dF[oF*7$$\"37+
+D6EjpeF[oF*7$F9F*-%&COLORG6&F>$\"\")!\"\"FbvFbv-F$6$7S7$F(F07$FFF07$F
JF07$FMF07$FPF07$FSF07$FVF07$FYF07$FfnF07$FinF07$F]oF07$F`oF07$FcoF07$
FfoF07$FioF07$F\\pF07$F_pF07$FbpF07$FepF07$FhpF07$F[qF07$F^qF07$FaqF07
$FdqF07$FgqF07$FjqF07$F]rF07$F`rF07$FcrF07$FfrF07$FirF07$F\\sF07$F_sF0
7$FbsF07$FesF07$FhsF07$F[tF07$F^tF07$FatF07$FdtF07$FgtF07$FjtF07$F]uF0
7$F`uF07$FcuF07$FfuF07$FiuF07$F\\vF0F8F_v-F$6$7S7$F(F37$FFF37$FJF37$FM
F37$FPF37$FSF37$FVF37$FYF37$FfnF37$FinF37$F]oF37$F`oF37$FcoF37$FfoF37$
FioF37$F\\pF37$F_pF37$FbpF37$FepF37$FhpF37$F[qF37$F^qF37$FaqF37$FdqF37
$FgqF37$FjqF37$F]rF37$F`rF37$FcrF37$FfrF37$FirF37$F\\sF37$F_sF37$FbsF3
7$FesF37$FhsF37$F[tF37$F^tF37$FatF37$FdtF37$FgtF37$FjtF37$F]uF37$F`uF3
7$FcuF37$FfuF37$FiuF37$F\\vF37$F9F3F_v-F$6$7S7$F(F-7$FFF-7$FJF-7$FMF-7
$FPF-7$FSF-7$FVF-7$FYF-7$FfnF-7$FinF-7$F]oF-7$F`oF-7$FcoF-7$FfoF-7$Fio
F-7$F\\pF-7$F_pF-7$FbpF-7$FepF-7$FhpF-7$F[qF-7$F^qF-7$FaqF-7$FdqF-7$Fg
qF-7$FjqF-7$F]rF-7$F`rF-7$FcrF-7$FfrF-7$FirF-7$F\\sF-7$F_sF-7$FbsF-7$F
esF-7$FhsF-7$F[tF-7$F^tF-7$FatF-7$FdtF-7$FgtF-7$FjtF-7$F]uF-7$F`uF-7$F
cuF-7$FfuF-7$FiuF-7$F\\vF-7$F9F-F_v-F$6$7S7$F*F(7$F*$\"3Hmmmm;')=()!#>
7$F*$\"3RLLLe'40j\"FH7$F*$\"3mmmm;6m$[#FH7$F*$\"3fmmm;yYULFH7$F*$\"3%H
LL$eF>(>%FH7$F*$\"3Qmmm\">K'*)\\FH7$F*$\"3P*****\\Kd,\"eFH7$F*$\"3-mmm
\"fX(emFH7$F*$\"3.*****\\U7Y](FH7$F*$\"3'QLLLV!pu$)FH7$F*$\"3xmmm;c0T
\"*FH7$F*$\"3#*******H,Q+5F[o7$F*$\"3)*******\\*3q3\"F[o7$F*$\"3)*****
**p=\\q6F[o7$F*$\"3mmm;fBIY7F[o7$F*$\"3GLLLj$[kL\"F[o7$F*$\"3?LLL`Q\"G
T\"F[o7$F*$\"3!*****\\s]k,:F[o7$F*$\"39LLL`dF!e\"F[o7$F*$\"33++]sgam;F
[o7$F*$\"3/++]<ep[<F[o7$F*$\"3QLLLe/TM=F[o7$F*$\"3JLL$eDBJ\">F[o7$F*$
\"3immmTc-)*>F[o7$F*$\"3Mmm;f`@'3#F[o7$F*$\"3y****\\nZ)H;#F[o7$F*$\"3Y
mmmJy*eC#F[o7$F*$\"3')******R^bJBF[o7$F*$\"3f*****\\5a`T#F[o7$F*$\"3o*
***\\7RV'\\#F[o7$F*$\"3k*****\\@fke#F[o7$F*$\"3/LLL`4NnEF[o7$F*$\"3#**
*****\\,s`FF[o7$F*$\"3[mm;zM)>$GF[o7$F*$\"3$*******pfa<HF[o7$F*$\"3#HL
Leg`!)*HF[o7$F*$\"3w****\\#G2A3$F[o7$F*$\"3;LLL$)G[kJF[o7$F*$\"3#)****
\\7yh]KF[o7$F*$\"3xmmm')fdLLF[o7$F*$\"3bmmm,FT=MF[o7$F*$\"3FLL$e#pa-NF
[o7$F*$\"3!*******Rv&)zNF[o7$F*$\"3ILLLGUYoOF[o7$F*$\"3_mmm1^rZPF[o7$F
*$\"34++]sI@KQF[o7$F*$\"34++]2%)38RF[oF,F_v-F$6$7S7$F0F(7$F0Fe`l7$F0Fi
`l7$F0F\\al7$F0F_al7$F0Fbal7$F0Feal7$F0Fhal7$F0F[bl7$F0F^bl7$F0Fabl7$F
0Fdbl7$F0Fgbl7$F0Fjbl7$F0F]cl7$F0F`cl7$F0Fccl7$F0Ffcl7$F0Ficl7$F0F\\dl
7$F0F_dl7$F0Fbdl7$F0Fedl7$F0Fhdl7$F0F[el7$F0F^el7$F0Fael7$F0Fdel7$F0Fg
el7$F0Fjel7$F0F]fl7$F0F`fl7$F0Fcfl7$F0Fffl7$F0Fifl7$F0F\\gl7$F0F_gl7$F
0Fbgl7$F0Fegl7$F0Fhgl7$F0F[hl7$F0F^hl7$F0Fahl7$F0Fdhl7$F0Fghl7$F0Fjhl7
$F0F]il7$F0F`il7$F0F-F_v-F$6$7S7$F3F(7$F3Fe`l7$F3Fi`l7$F3F\\al7$F3F_al
7$F3Fbal7$F3Feal7$F3Fhal7$F3F[bl7$F3F^bl7$F3Fabl7$F3Fdbl7$F3Fgbl7$F3Fj
bl7$F3F]cl7$F3F`cl7$F3Fccl7$F3Ffcl7$F3Ficl7$F3F\\dl7$F3F_dl7$F3Fbdl7$F
3Fedl7$F3Fhdl7$F3F[el7$F3F^el7$F3Fael7$F3Fdel7$F3Fgel7$F3Fjel7$F3F]fl7
$F3F`fl7$F3Fcfl7$F3Fffl7$F3Fifl7$F3F\\gl7$F3F_gl7$F3Fbgl7$F3Fegl7$F3Fh
gl7$F3F[hl7$F3F^hl7$F3Fahl7$F3Fdhl7$F3Fghl7$F3Fjhl7$F3F]il7$F3F`il7$F3
F-F_v-F$6$7S7$F-F(7$F-Fe`l7$F-Fi`l7$F-F\\al7$F-F_al7$F-Fbal7$F-Feal7$F
-Fhal7$F-F[bl7$F-F^bl7$F-Fabl7$F-Fdbl7$F-Fgbl7$F-Fjbl7$F-F]cl7$F-F`cl7
$F-Fccl7$F-Ffcl7$F-Ficl7$F-F\\dl7$F-F_dl7$F-Fbdl7$F-Fedl7$F-Fhdl7$F-F[
el7$F-F^el7$F-Fael7$F-Fdel7$F-Fgel7$F-Fjel7$F-F]fl7$F-F`fl7$F-Fcfl7$F-
Fffl7$F-Fifl7$F-F\\gl7$F-F_gl7$F-Fbgl7$F-Fegl7$F-Fhgl7$F-F[hl7$F-F^hl7
$F-Fahl7$F-Fdhl7$F-Fghl7$F-Fjhl7$F-F]il7$F-F`il7$F-F-F_v-F$6$7SF57$F6F
e`l7$F6Fi`l7$F6F\\al7$F6F_al7$F6Fbal7$F6Feal7$F6Fhal7$F6F[bl7$F6F^bl7$
F6Fabl7$F6Fdbl7$F6Fgbl7$F6Fjbl7$F6F]cl7$F6F`cl7$F6Fccl7$F6Ffcl7$F6Ficl
7$F6F\\dl7$F6F_dl7$F6Fbdl7$F6Fedl7$F6Fhdl7$F6F[el7$F6F^el7$F6Fael7$F6F
del7$F6Fgel7$F6Fjel7$F6F]fl7$F6F`fl7$F6Fcfl7$F6Fffl7$F6Fifl7$F6F\\gl7$
F6F_gl7$F6Fbgl7$F6Fegl7$F6Fhgl7$F6F[hl7$F6F^hl7$F6Fahl7$F6Fdhl7$F6Fghl
7$F6Fjhl7$F6F]il7$F6F`il7$F6F-F_v-F$6$7S7$F9F(7$F9Fe`l7$F9Fi`l7$F9F\\a
l7$F9F_al7$F9Fbal7$F9Feal7$F9Fhal7$F9F[bl7$F9F^bl7$F9Fabl7$F9Fdbl7$F9F
gbl7$F9Fjbl7$F9F]cl7$F9F`cl7$F9Fccl7$F9Ffcl7$F9Ficl7$F9F\\dl7$F9F_dl7$
F9Fbdl7$F9Fedl7$F9Fhdl7$F9F[el7$F9F^el7$F9Fael7$F9Fdel7$F9Fgel7$F9Fjel
7$F9F]fl7$F9F`fl7$F9Fcfl7$F9Fffl7$F9Fifl7$F9F\\gl7$F9F_gl7$F9Fbgl7$F9F
egl7$F9Fhgl7$F9F[hl7$F9F^hl7$F9Fahl7$F9Fdhl7$F9Fghl7$F9Fjhl7$F9F]il7$F
9F`ilF_`lF_v-%)POLYGONSG6$7&F_]lFe\\mFeil7$F(F(-F`v6&F>$\"#**!\"#F[jm$
\"#!*F]jm-Feim6$7&7$F0F3F2F]`mFeilFiim-Feim6$7&F2F[]lFdfmF]`mFiim-%+AX
ESLABELSG6%Q!6\"Fjjm-%%FONTG6#%(DEFAULTG-%%VIEWG6$;F(F9F_[n" 1 2 0 1 
10 0 2 9 1 4 2 1.000000 45.000000 45.000000 0 0 "Curve 1" "Curve 2" "C
urve 3" "Curve 4" "Curve 5" "Curve 6" "Curve 7" "Curve 8" "Curve 9" "C
urve 10" "Curve 11" "Curve 12" "Curve 13" "Curve 14" }}}{PARA 0 "" 0 "
" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 
0 "" {MPLTEXT 1 0 139 "Delta := (6-0)/3;\nupperRiemannSum := f(0.5)*De
lta + f(2)*Delta + f(2)*Delta;\nupperRiemannSum := subs(\{f(0.5)=4, f(
2)=3\}, upperRiemannSum); " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%&Delta
G\"\"#" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%0upperRiemannSumG,&*&\"\"#
\"\"\"-%\"fG6#$\"\"&!\"\"F(F(*&\"\"%F(-F*6#F'F(F(" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>%0upperRiemannSumG\"#?" }}}{PARA 0 "" 0 "" {TEXT -1 0 
"" }}}{SECT 0 {PARA 3 "" 0 "" {TEXT 557 17 "2. The expression" }}
{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 28 "         \+
                   " }{OLE 1 217603 1 "[xm]Br=WfoRrB:::wk;nyyI;G:;:J<j
:J:ZJJ;j:JyyyyyI<:^:f:n:vyyyyy=:::::::::::::::::::::::::::::::::::::::
:::::::::::::::::::::::::::::jxyyyyyMA:wAwyyyqx;:K:M:O:Q:S:UJ:n;v;;JB>
Z:F<N<V<^<f<n<v<>=F=N=V=^=f=n=v=>><jJJKjKJLjLJMjMJNjNJOjOJPjPJQjQJR<Z:
F@N@V@^@f@n@v@>AFANAVA^AfAnA;jYJZB:=<?<A<C<E<G<I<K<M<O<Q<S<U<W<Y<[\\:F
DNDVD^DfDnDvD>EFENEVE^EfEnEvE>F<jjJkjkJljlJmjmJnjnJojoJpjpJqjqJrB:]=_=
a=c=e=g=i=k=m=o=q=s=u=w=y=;^:NDYmq^H;k\\nGcMsFI>:::::::JEf:yyyxIN:<J?V
:>:;`:Z@[::J:qs=xJCxy]Aj;J:@:<:=j[vGUMrvC?MoJ::::::::JCNZ;^:vYxI>:<:::
:::j`J:j:vCSmlF@[KaFFcmnnHEM:>:::::::oJ;@j:j;B:yayA:<::::::IZ:^jyV:>:=
:jRj^^HEmpnCfGEM:>::::::n=?R:yyyyyy:>:<::::::?:EJ:>:F:;JyKy;vY::::::::
::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
::::F:wyyAb<vYxY?V:<J:>R<:Tn=JbDNsPqs\\`A:::ZnIalHH>::::::::::j:JlJ:::
:::::::F:D:<:::::::::::::::::::::::::::::::::::::::::::::::::AMW^E[Lsv
GIMsFF>>=^:NJ<j;K<=:E^:nJvJ>KFKNK<j?K@k@KAkAKBC:]>_>a>c>e>g>i>kN:FMNMV
M^MfMnMvM>n:B:=???A?C?E?G?I?K?M?O?Q?S?U?W?Y?[_:FPNPVP^PfPnPvP>QFQNQVQ^
QfQnQvQ>R<jZK[k[K\\k\\K]k]K^k^K_k_K`k`KakaKbC:]@_@a@c@e@g@i@k@m@o@q@s@
u@w@yH:>V<jjKkkkKlklKmkmKnknKokoKpkpKqkq=:[a:FX;JsksKtktKukuKvkv?:oQ:V
Y^YfYny:jy=:;R:FZ;J;@J:VZ;B:CR:fZ;J=@Z:vZ;J>@:MR:N[;j?@:SR:f[;JA@:YR:>
\\;B:]R:N\\;jC@:cR:f\\;JE@:iR:>];jF@:oR:V];JH@:uR:n];jI@:;S:F^;JK@:AS:
^^;jL@:GS:v^;JN@:MS:N_;jO@:SS:f_;JQ@:YS:>`;jR@:_S:V`;JT@:eS:n`;jU@:kS:
Fa;JW@:qS:^a;jX@:wS:va;JZ@:=T:Nb;j[@:CT:fb;J]@:IT:>c;j^@:OT:Vc;J`@:UT:
nc;ja@:[T:Fd;Jc@:aT:^d;jd@:gT:vd;Jf@:mT:Ne;jg@:sT:fe;Ji@:yT:>f;jj@:?U:
Vf;Jl@:EU:nf;jm@:KU:Fg;Jo@:QU:^g;jp@:WU:vg;Jr@:]U:Nh;js@:cU:fh;Ju@:iU:
>i;jv@:oU:Vi;Jx@:uU:ni;jy@:;V:Fj;J;A:AV:^j;j<A:GV:vj;J>A:MV:Nk;j?A:SV:
fk;JAA:YV:>l;jBA:_V:Vl;JDA:eV:nl;jEA:kV:Fm;JGA:qV:^m;jHA:wV:vm;JJA:=W:
Nn;jKA:CW:fn;JMA:wyyyQyky;::::::::::::::::::::::::::::::::::::::::::::
:::::::::::::J:ym;NbGofyV:;J:n`:JN<:oi:fe:j:<JFJ:>`yV:>:::yyyyyy::::::
::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
::::::::::::::::::::::::>:yay=::::::::::::::::::::::::::::::::::::::::
::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::J:Zy=::::::
::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
:::::::::::::::::::::::J:Zy=::::::::::::::::::::::::::::::::::::::::::
::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
:::::::::::::::::::::::::::::::::::::::::::::::::::::::::J:Zy=::::::::
::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
:::::::::::::::::::::J:Zy=::::::::::::::::::::::::::::::::::::::::::::
::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
:::::::::::::::::::::::::::::::::::::::::::::::::::::::J:Zy=::::::::::
::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
:::::::::::::::::::J:Zy=::::::::::::::::::::::::::::::::::::::::::::::
::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
:::::::::::::::::::::::::::::::::::::::::::::::::::::J:Zy=::::::::::::
::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
:::::::::::::::::J:Zy=::::::::::::::::::::::::::::::::::::::::::::::::
::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
:::::::::::::::::::::::::::::::::::::::::::::::::::J:Zy=::::::::::::::
::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
:::::::::::::::J:Zy=::::::::::::::::::::::::::::::::::::::::::::::::::
::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
:::::::::::::::::::::::::::::::::::::::::::::::::J:Zy=::::::::::::::::
::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
:::::::::::::J:Zy=::::::::::::::::::::::::::::::::::::::::::::::::::::
::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
:::::::::::::::::::::::::::::::::::::::::::::::J:Zy=::::::::::::::::::
::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
:::::::::::J:Zy=::::::::::::::::::::::::::::::::::::::::::::::::::::::
::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
:::::::::::::::::::::::::::::::::::::::::::::J:Zy=::::::::::::::::::::
::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
:::::::::J:Zy=::::::::::::::::::::::::::::::::::::::::::::::::::::::::
::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
:::::::::::::::::::::::::::::::::::::::::::J:Zy=::::::::::::::::::::::
::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
:::::::J:Zy=::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
:::::::::::::::::::::::::::::::::::::::::J:Zy=::::::::::::::::::::::::
::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
:::::J:Zy=::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
:::::::::::::::::::::::::::::::::::::::J:Zy=::::::::::::::::::::::::::
::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
:::J:Zy=::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
:::::::::::::::::::::::::::::::::::::J:Zy=::::::::::::::::::::::::::::
::::::::::::::::::::::::::::::::::::::::::::::::::J^lsiC:;:Zy`HyyyxI::
BLvyy`hyyyyyY:::::::::::::\\>;Z::jY;yA::>CxIry::::::::::::::::::::::::
::::::::::::::::::::>C<:;:Zy<xI::BLvYjy;::::::::::::BL>:<::y?vY::J^ryZ
y=:::::::::::::::::::::::::::::::::::::::::::J^B:>::xEry::ZBky;yA:::::
:::::::ZBK:B::vQjy;::K\\y=xI::::::::::::::::::::::::::::::::::::::::::
::::::::::::::::::::::::::::::::::::::K\\:J::riZy=::\\>yAvY:::::::::::
:::::J^B:>::xEry::ZBky;yA:::::::::>:yay=::::::::::::::::::::::::::::::
:::::::::::::::::::::::::::::::::::::::::::::::::xG;BLsFaKlyyyisy:::cu
iyI:;B:yyic=yA:::::::::::::vU<J^:xGyA::BW>Z::ry:::::::::::::::::::::::
:::::::::::::::::::::ZYM:\\>jisy:::c]:>::yA:::::::::::::vU<J^:xGyA::BW
>Z::ry::::::::::::::::::::::::::::::::::::::::::::ZYM:\\>jisy:::c]:>::
yA:::::::::::::vU<J^:xGyA::BW>Z::ry:::::::::::::::::::::::::::::::::::
:::::::::::::::::::::::::::::::::::::::::::::ZYM:\\>jisy:::c]:>::yA:::
:::::::::::::ZYM:\\>jisy:::c]:>::yA:::::::::>:yyyyyy::::::::::::::::::
::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::^HxWH]ny
yyyyI::Bayxy;J^<:xEvY::::::::::::::LA:yA::^M::xI::::::::::::::::::::::
:::::::::::::::::::::::c=Zy=::lC::yA:::::::::::::Zn;jy;::s>:Zy=:::::::
:::::::::::::::::::::::::::::::::::::Jt:ry::ZV<:jy;:::::::::::::BW:vY:
:JH;:ry:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
::::::::::::::::::^H:xI::Ba::vY:::::::::::::::::Jt:ry::ZV<:jy;::::::::
:;jyyyyyI:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
:::::::::::::::::::c]Y=xI::ywyyI:LQ:<Z:jyyEvY::::::::::::::LA:yA:ZyL::
;Zy=xI:::::::::::::::::::::::::::::::::::::::::::::c=Zy=:jYC:Z:jy;yA::
:::::::::::Zn;jy;:ri>:J:ryZy=:::::::::::::::::::::::::::::::::::::::::
:::Jt:ry::vQ<:B:vYjy;:::::::::::::BW:vY::xE;:>:xIry:::::::::::::::::::
::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::^H:xI::y
_::<:yAvY:::::::::::::::::Jt:ry::vQ<:B:vYjy;:::::::::;jyyyyyI:::::::::
:::::::::::::::::::::::B:cui>Z::xEry:ZYyYsFWsvyyyqvY::::::::::::::::::
::::::::::::::::::::::^HxWH[y=:xwy?ZBC:>:jyyEvY::::::::::::::LAlCvY:ji
yi::<:ryZy=::::::::::::::::::::::::::::::::::::::::::::JtJH[y=:xwy?:J:
:yAvY::::::::::::::LAlCvY:jiyi::<:ryZy=:::::::::::::::::::::::::::::::
:::::::::::::JtJH[y=:xwy?:J::yAvY::::::::::::::LAlCvY:jiyi::<:ryZy=:::
::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
:::::::JtJH[y=:xwy?:J::yAvY:::::::::::::::::JtJH[y=:xwy?:J::yAvY::::::
:::J:<jyyyyyI:::::::::::::::::::::::::::::::::y_n?ZnwyyyQxI::<Jt^mB?:x
GyA::::::::::::::::::::::::::::::::::::::::cui^Myay=jiyi:>CB::vyy\\yyY
::::::::::::::LAlCvY:xwy?:J::ryZy=::::::::::::::::::::::::::::::::::::
::::::::JtJH[y=jiyi::<::yAvY::::::::::::::LAlCvY:xwy?:J::ryZy=::::::::
::::::::::::::::::::::::::::::::::::JtJH[y=jiyi::<::yAvY::::::::::::::
LAlCvY:xwy?:J::ryZy=::::::::::::::::::::::::::::::::::::::::::::::::::
::::::::::::::::::::::::::::::JtJH[y=jiyi::<::yAvY:::::::::::::::::JtJ
H[y=jiyi::<::yAvY:::::::::J:<Zyyyy=::::::::::::::::::::::::::::::::jiC
a:xI:J^B:<JH]>xGyA:::::::::::::::::B:cmY?ZyuyyA::::::::::::::::::::^Hx
WH[y=J:B:>:J^BLcEWyyicuyvY:jiyi:>Cryy?xI:::::::::BWBajy;B:c=<:BL;Zn;ry
::::::::::::::::::::::Z:jY?:xyy;::::::::::::::::::::c]Y=xI:;Z:J::KD:^H
ryvY:jiyi:>CryZy=:::::::::LAlCvY:<JtZ::\\N:BW:xI::::::::::::::::::::::
B:vQ;ZyyY::::::::::::::::::::JtrqZy=J:B:>:J^<:c=xIyA:vuyE:K<xIry::::::
:::Zn[V<yAZ:^HB:ZB?:LAZy=:::::::::::::::::::::::::::::::::::::::::::::
:::::::::::::<:yO:ryyA::::::::::::::::::::^HxGry:>:<:;:>c:JtZymy;::::r
qyQ:\\>vYjy;:::::::::c=s>xI:;BWJ::KD:^H:yA:::::::::>Z:vyyyyy=:::::::::
:::::::::::::::::::::::jiyiV<ry:BW>:;B:^MrqvY::::::::::::::::ZnK::vUxI
::::::::::::::::::::JtJH[y=\\>B::vyyDLsvqyyicuyvY::J:LAvQryyA::::::::Z
nki;yA>C<:;:ZyM^ryvYxI:::::::::::::::::::::BW>Z:Bajiyiy=::::::::::::::
::::::^H^MryZBK:B::vY\\>yaymy;::;BWjY[yyY:::::::::LAy@vYJ^B:>::xIK\\ym
ysy:::::::::::::::::::::ZnK:<ZV<yxyxI::::::::::::::::::::JtJH[y=\\>;Z:
:jyCLvYxIyA::>Zn;y?xyy;::::::::BWvUjy;K\\:J::ry>CxIyay=:::::::::::::::
::::::::::::::::::::::::::::::::::::::::::LA;B:lCvuyuy::::::::::::::::
:::::c=s>xIBL>:<::yaBkysyvY::::::<JtZy<yyy:::::::::^HxGryZBK:B::vY\\>y
aymy;:::::::::;B:yyyyyy:::::::::::::::::::::::::::::::::vuyEa:xIJHyg:B
L;J:<:s>xGyA::::::::::::::::K\\:B:y?xyy;:::::::::::::::::::::c]YaMry^H
<:;:ZYamB[BkyyEvY::jiyi:>C:ry::::::::ZnkimCvYLA;B:<::y@>C:xI::::::::::
:::::::::::K\\:jY[yyY:::::::::::::::::::::JtrqZyMtB:>::xGBLvYjy;::yxy<
J^:Zy=::::::::LAyHajyCW>Z:B::vUJ^:ry:::::::::::::::::::::>C<:y?xyy;:::
::::::::::::::::::c]Y=xIc]:J::rqZBky;yA::vuyE:K<:xI::::::::BWvuV<yanK:
<Z::ji;K<Zy=::::::::::::::::::::::::::::::::::::::::::::::::::::::::J^
B:vQryyA:::::::::::::::::::::^HxGry^H<:;:ZY=\\>yAvY::::::xwy?ZB;:yA:::
:::::^HxWH[yMtB:;J::rqZB;jy;:::::::::;jywyy=::::::::::::::::::::::::::
::::::jiyiV`HZy]yxY;JtJ:BWKLHMQtxyyyGyA:::::::::::::::BL>:;Bajisy:::::
:::::::::::::::::c=s>J:B::vUjyCLvYc]yyY:::LAB:vyy<yA:::::::Znki;B:>::x
Gry>C:xI::::::::::::::::::::BL>:lCvuyuy::::::::::::::::::::::c=s>J:B::
vUjyCLvYjy;::BWZ:jy;yA:::::::Znki;B:>::xGry>C:xI::::::::::::::::::::BL
>:lCvuyuy::::::::::::::::::::::c=s>J:B::vUjyCLvYjy;::BWZ:jy;yA:::::::Z
nki;B:>::xGry>C:xI::::::::::::::::::::::::::::::::::::::::::::::::::::
::::BL>:lCvuyuy::::::::::::::::::::::c=s>J:B::vUjyCLvYjy;::::::c=>:xIr
y::::::::^HxG:;Z::ji;yaB;jy;:::::::::;jyyyyyI:::::::::::::::::::::::::
::::::::yxylCZyyU<J^Z:J^rqyHasFWs>vY:::::::::::::::^H<J:<J:ryy?xI:::::
:::::::::::::::::c]YamB_mYE:\\>;B:Zy<yyyZB[y<yA::ZYyY;BLJ^ryyHayyyyyy:
::::::ZnkimS^J:<:<J::y?xyy;K<y?xI::::::::::::::::::::c]:B:;ZyyQry:::::
:::::::::::::::::^HxGB:\\><:rijyyIBLrijy;::rqyQ:\\>>CxyiwYxI:::::::BWv
uV@C>Z:Z:>:jY[yyYJ^jY[y=:::::::::::::::::::JtB:<J:ryy?xI::::::::::::::
::::::::c]Y=<ZB[::xEvyy=\\>xEvY:::xwy?ZB;K\\yyUyay=:::::::LAyHaK<;B:B:
;:vQryyA>CvQry::::::::::::::::::::::::::::::::::::::::::::::::::::::::
^H<Z:>:xyY[y=:::::::::::::::::::::JtrqZ:BLB:Zy<yyyZB[y<yA::::::vuyE:K<
\\>yyqxIyA:::::::^HxWH]><J:J:<:rijyyIBLrijy;:::::::::;jyyiy=::::::::::
::::::::::::::::::::::jiyiV<y`yAZn[:>:jyyeYyyyaM:yA::::::::::::::riyQ:
<Jt<:s>xGyA::::::::::::::::::::::c]V`mBC:c=;:^MxiYmy;\\>^hymy;:::K\\:B
:;Zy<yyy:::::::ZnKHK:Z::lCyqisy:K\\y=xI:::::::::::::::::::riyQ:^H:jy;:
::::::::::::::::::::JtBaB:J::s^yuqvYZB;c=yA:::>C<Z:>:xEvyy=:::::::LAs>
;:<:BavYy`y=>CxIry:::::::::::::::::::ZyxY;Jt::yA::::::::::::::::::::::
c]V\\::;:^MxiYmy;\\>^HvY:::J^B:<J:rijyyI:::::::BW^M>:B:ZVlywUxIJ^ryZy=
:::::::::::::::::::::::::::::::::::::::::::::::::::::::xuy?:c=:vY:::::
:::::::::::::::::^HlC<:>:JHsyxGyABLJtjy;::::::BL>:;B:vQryyA:::::::^HlC
<:>:JHsyxGyABLvYjy;:::::::::;jyyyyyI:::::::::::::::::::::::::::::::::y
`V`HBLsN:>Z::xWHwYxwy_M:yA::::::::::::::B:c=<:y@vY::::::::::::::::::::
::JtB:;J::BWvYywyxI:\\>yQtjy;:::svq<ZBK:<:yyijy;::::::BW>:;B::^HvyyxYy
A:K<yGWry:::::::::::::::::::Z:^HB:vUjy;::::::::::::::::::::::c]:>:;:Zn
;ywyxI:\\>^HvY:::JHC:\\><:yyijy;::::::BW>:;B::^HvyyxYyA:K<yGWry:::::::
::::::::::::Z:^HB:vUjy;::::::::::::::::::::::c]:>:;:Zn;ywyxI:\\>^HvY::
:JHC:\\><:yyijy;::::::BW>:;B::^HvyyxYyA:K<yGWry:::::::::::::::::::::::
::::::::::::::::::::::::::::::::Z:^HB:vUjy;::::::::::::::::::::::c]:>:
;:Zn;ywyxI:\\>^HvY:::::::lC;J^J:ryy?xI:::::::c]:B:;:Zn[yyqyuy:BLric=yA
:::::::::>:yqyyI:::::::::::::::::::::::::y`n?CyyyywyxY:LA<J::K\\yyUyqy
yI::y`V`HcuiyH:>:jY;yaYMHsyxGyA::::::::::::::svq<J:\\>;B:vyy<yA:::::::
:::::::::::::::>Zn[:>:J^ryyHavyy=jiC:KLH[Ymy;::jYC:;BW>Z:jY[yyY:::::::
<JtJ:<:BL:vY:xG;BL:y`y=::::::::::::::::::^M>ZBK:<:yyijy;::::::::::::::
::::::::;BWB:;:>Cxyi[y=jiC:K<:yA:::y_:>Zn[:jY[yyY:::::::<JtJ:<:BL:vY:x
G;BL:y`y=::::::::::::::::::^M>ZBK:<:yyijy;::::::::::::::::::::::;BWB:;
:>Cxyi[y=jiC:K<:yA:::y_:>Zn[:jY[yyY:::::::<JtJ:<:BL:vY:xG;BL:y`y=:::::
:::::::::::::::::::::::::::::::::::::::::::::::::^M>ZBK:<:yyijy;::::::
::::::::::::::::;BWB:;:>Cxyi[y=jiC:K<:yA::::::ri>Z:^H>:xEvyy=::::::J:L
A<J::K<Zy=jiC:K<rqvY:::::::::>Z:vyyyyy=::::::::::::::::::::::::jiC:KL:
B:vQjy;K\\:B::yA:vU<:B:ZV<y`y]YMHMAxGyA::::::::::::::;BWJ:BWvYy_y=:ZB;
<::::s>xGyA:::::::::::::;:>::jyyEvY:<:B::vUjy;::y`:>CB:^Hvyyly;:::::<J
tZ:::xyY[y=J::;:ZY=xI::::::::BWyO^<:y@yyy:::::::>:J:BWryy_y=:ZB_MB::::
^MrqvY:::::::::::::>:J:::yyijy;B:Z::ji;yA::vU<J^Z:JtjyyEyA:::::B:c=<::
ryy?xI:;:>::xGry::::::::ZnK^<:y@xI:::::::;:>:LAxyYsy::BLs><::::s>xGyA:
::::::::::::;:>::jyyEvY:<:B::vUjy;::y`:>CB:^Hvyyly;:::::<JtZ:::xyY[y=J
::;:ZY=xI:::::::::::::::::::::::::::::::::::::::::::::BW>c:ji[y=:::::J
::;Zn[yyQxI::\\NH[::::JH[Ymy;::::::::::::J::;::vyy<yAZ::<::y@vY::::::x
G;BLJ:BWryy_y=:::::>Zn;;::vyy<yAZ::<::y@vY::::::::J:<jyyyyyI::::::::::
:::::::::::::::y`:>Cryy?xI:B:c=;rqZy=jYC:;BW>Z:JtryyyivYZyLt<JtrivY:::
::::::::::ZyL:Z:>:lCvUxI::Jtxe:B:;:::>CvUry:::::::::::::::::::::::::vU
<J^Z::xyYkyyI:::::::::::::::::::::::BW>c:ji[y=::::::xE;B:c=;ZV<y`y=::^
H<Z:>:::J^:ry:::::::::::::::::::::::::vU<J^Z::xyY[y=::::::::::::::::::
:::::LAK<y@xI::::::ri>Z:^H>:lCvUxI::JtB:<J::::K<Zy=:::::::::::::::::::
:::::jiC:K<<:ryy?xI::::::::::::::::::::::BW>CvUry:::::::::::::::::::::
::::::::::::::Zn;:xI:::::ri>Z:^H>:lCvUxI::JtB:<J::::K<Zy=:::::::::::::
:::::::::::::::xG;BLJ::yyijy;:::::::::::::::::::::::;B:yyyyyy:::::::::
::::::::::::::::vU<J^vuV@CvY::<JtJ:lCvUxI<J^>:<:BLrqjy;;BWJ::y_yuyyA::
::::::::::ZVxU<J^B:;ZV<y`y=::ZB_M;J:<:::rqZy=::::JtBL;jy;yA:::::::::::
::::::Z:^HB:ZY=xI:::::::::::::::::::::::BW:Zy=::::::lC<J^B:;ZV<y`y=::Z
B_M>Z::::xGry:::::^H\\N:vYjy;:::::::::::::::::B:c=<:rqZy=:::::::::::::
::::::::::LA:ry::::::ZV\\:>C<J:Bajisy:::BLs>;B:::ZY=xI:::::c]B?:yAvY::
::::::::::::::::<JtZ::xGry::::::::::::::::::::::Zn;:xI::::::::::::::::
:::::::::::::::::::BW:Zy=:::::lC<J^B:;ZV<y`y=::ZB_M>Z::::xGry:::::^H\\
N:vYjy;:::::::::::::::::::::;BWJ::y@vY:::::::::::::::::::::::J:<jyyyyy
I:::::::::::::::::::::::::y`n?CvQxI:Jtxe:B:;ZnkywQxI::::::::::::::::::
:::\\NH[::xEvyy=:::J^ricE:ry:^MxUt\\nyyiy=::::JtBL;ZY]yyY:::::::::::::
:::::<JtZ::xEvyy=:::::::::::::::::::::::LAK<Zy=::::::\\NH?:<:rijyyI:::
:K\\yD:ry:^MBLry:::::^H\\N::vY::::::::::::::::::<:B:Zy<yyy::::::::::::
:::::::::::ZnK^:ry::::::ZB_M;Z::xEvyy=:::J^ri<:xI:s>\\>xI:::::c]B?::yA
:::::::::::::::::Z::<:rijyyI::::::::::::::::::::::BW>C:xI::::::::B:Z:j
i;yA::::Z::<:y@vY:::::<:B:vUjy;:::::::BW:Zy=:::::\\NH?:<:rijyyI::::K\\
yD:ry:^MBLry:::::^H\\N::vY:::::::::::::::::::::J::;:vQryyA::::::::::::
:::::::::::>Z:vyyuy:::::::::::::::::::::::::vUlStjisy:y`:>CB:ZV<y`y=::
::::::::::::::::::ZB_M;J:<:rijyyI::::B:cmY?:vY:::::::JtBL;ZY]yyY::::::
::::::::::::<:;Z::xEvyy=:::::::::::::::::::::::LAK<Zy=::::::\\NH[::xEv
yy=::::<:y?vY:::::::JtBL;:jy;:::::::::::::::::B:>:<:rijyyI::::::::::::
:::::::::::BW>C:xI::::::BLs><:rijyyI::::B:vQjy;:::::::c]B?::yA::::::::
:::::::::Z:J:B:Zy<yyy::::::::::::::::::::::ZnK^:ry::::::::>:J::ryyoysy
::::>:J::ryZy=:::J::;:ZyyyyyY::::::::LAK<y@xI:::::BLs><:rijyyI::::B:vQ
;:yA:::::::^H\\N::vY:::::::::::::::::::::J:B:>:jY[yyY:::::::::::::::::
::::::J:<jyyiy=::::::::::::::::::::::::::jYyi:BW>Z:::xyYwYxI:::::::::B
:c=;B::::Zy<xI:::::B:Z::xEry::::ZYM:\\^y`Hry:::::::^H\\>xGvY::::::::::
::::::::<JtZ::xEvyy=::::::::::::::::::::J^lC>:::::ji;yA:::Z::<:riZy=::
::xG;BL:xI:::::::c]B?::yA:::::::::::::::::Z:^HB:Zy<yyy::::::::::::::::
:::::>cV<;:::::vUjy;:::B:Z::xEry::::ZYM:\\>Zy=::::::JtBL;:jy;:::::::::
::::::::B:c=<:rijyyI::::::::::::::::::::::BW>C:xI:::::::rq>ZBC:>::xGry
:::ZYM::;:ZY=xI:::rq>:J::ryyyyyA:::::>cV<;:::::vUjy;::B:c=<:riZy=::::x
G;BLxEry:::::::^H\\N:rqjy;:::::::::::::::::::::;BWJ::y?xyy;:::::::::::
::::::::::::;B:yyyxI::::::::::::::::::::::::::y`:>C;Z:::ji;yA:::::::::
::::::::::::Z:^H>Z::xEry:::::^mYE:;BLyHaK<yA::::::^H\\>xGvY::::J:>Z:::
:::::::jyyyyyI::B:c=<:riZy=::::<J:>::::::::::xIyA:::::::ZnK^ji[y=:::::
:<JtZ::xEvyy=::::JHK:\\>jy;::::::c]B;jy;::::;J:<::::::::::yyyyyy::Z:^H
B:Zy<xI::::B:;J::::::::::ryvY::::::::LAK<y@xI::::::B:c=<:rijyyI:::::s>
;BL:yA::::::^H\\>:yA::::>:;B::::::::::vyyyyy=::<JtZ::xEry::::Z:>:;::::
:::::Zymy;::::KDaJ::::::y@vY:::::J:LA>::xyY[y=:::J::;:Zy=xI::::;:>::xy
ywY::::::::LAKD:vUry:::::Z::<:rijyyI:::::s>;BL:yA::::::^H\\>:yA::::>:;
B::::::::::vyyyyy=:::::J:LA>:jY;yA::::>Z:B::::::::::vYxI::::::::;jysy:
::::::::::::::::::::::::ZYM:\\>>::JH[Ymy;::::::::::::::::::::::<JtJ:<:
rijyyI:::::B:ZyyQry:::ZB_MB:::::ZY=xI::;B:<::::::::::yyyxI::B:c=<:riZy
=::::<J:>::::::::::xIyA:::::::ZnK^<:y@xI::::::B:c=<:rijyyI:::::B:ZyyQr
y:::ZB_MB:::::ZY=xI::;B:<::::::::::yyyxI::B:c=<:riZy=::::<J:>:::::::::
:xIyA:::::::ZnK^<:y@xI::::::B:c=<:rijyyI:::::B:ZyyQry:::ZB_MB:::::ZY=x
I::;B:<::::::::::yyyxI::B:c=<:riZy=::::<J:>::::::::::xIyA::::::ZnK^<:y
@xI::::::::B:c=<:y@vY:::::<:B:vUjy;::::B:Z:ji;yA:::::::Zn;:xI:::::B:Z:
:xEvyy=:::::<:ryy?xI:::BLs><:::::rqZy=:J:<Z::::::::::jyyiy=:::::J:LA>:
jY;yA::::>Z:B::::::::::vYxI::::::::;jysy:::::::::::::::::::::::::ZB;;B
::^MrqvY:::::::::::Z:^HB::::Zy<yyy:::::Z::<:riZy=:::::\\>BWvYy_y=:::::
^H\\N:rqjy;:::::::::::::::::B:Z::xGry:::::::::::::::::::::::Zn;:xI::::
::B:Z::xEvyy=:::::\\NH[n[yyQxI:::::JtBL;ZY=yA:::::::::::::::::Z::<:rqZ
y=:::::::::::::::::::::::LA:ry::::::Z::<:rijyyI:::::BLs>LAxyYsy::::::c
]B?:xGvY::::::::::::::::::<:B:ZY=xI::::::::::::::::::::::BW:Zy=:::::::
::::::::::::::::::::::::::::LA:ry:::::Z::<:rijyyI:::::BLs>LAxyYsy:::::
:c]B?:xGvY:::::::::::::::::::::J::;:vUjy;:::::::::::::::::::::::;B:yyy
yyy:::::::::::::::::::::::::vU<J^Z:JH[Ymy;JHmsiyyyyEyA::::::::::::::::
:::::BLs>;B:Zy<yyy:::::ZnK:<Z:ji;yA:::::^H\\N:rqjy;:::::::::::::::::y`
:>CB:>c::ry:::::::::::::::::::::::Zn;:xI::::::BLs><:rijyyI:::::BW>Z:B:
vUjy;:::::c]B?::yA:::::::::::::::::vU<J^Z:J^:ry:::::::::::::::::::::::
Zn;:xI::::::BLs><:rijyyI:::::BW>Z:B:vUjy;:::::c]B?::yA:::::::ZVxU;J^B:
;:vyy<yA:::::vU<J^Z:J^ryy@xI::::::::::::::::::::::BW:Zy=::::::::::::::
:::::::::::::::::::::LA:ry:::::ZB_M>Z::xEvyy=:::::LA;B:<:y@vY:::::JtBL
;:jy;::::::::::::::::::::rq>ZB;;ZB;jy;:::::::::::::::::::::::;B:yyyyyy
:::::::::::::::::::::::::Z:^H>ZV<y`y=ZyLt<JtrivY:::::::::::::::::::::Z
nwQ;B:<:Bajisy::BWvyy`Hxyy;BLs><:s>xGyA:::::c]B?:xGvY:::::::::::::::::
jiC:K<<:c=yyiyqy;:::::::::::::::::::::::LAK<y@xI::::::BW>Z:B:ZV<y`y=:Z
nkyyUtjy;BLs><:s>xGyA:::::c]B?::yA::::::::Z:^HB:vUjy;:::::y`:>CB:^Hvyy
xYyA:::::::::::::::::::::::BW>CvUry::::::ZnK:<Z::lCvUxI::LAyyic=yAZB_M
B:^MrqvY:::::^H\\N::vY:::::::J^lC>:xyY[:^HrivYyyy:::::vU<J^Z:JtjyyuywY
::::::::::::::::::::::ZnK^<:y@xI:::::::::::::::::::::::::::::::::::BW:
Zy=:::::LA;B:<:Bajisy::BWvyy`HvY:\\NH[:JH[Ymy;::::JtBL;:jy;::BLs><::::
s>xGyILZ::jY[yyY::J^ryy?xI:::rq>ZB;;Zn[yyqyuy::::::::::::::::::::::::;
B:yqyyI:::::::::::::::::::::::::BL>:;riZy=:<Jt^h:>:xEyA:::::::::::::::
::::::ri>Z:^H<J:Bajisy::ri>c:^hyyuV\\yMtB:<J::s>xGyA:::::c]BC:xGvY::::
:::::::::::::jYC:LA<:y_yuyyA::::::::::::::::::::::::::::::::ZyL::;ZV<y
`y=:ZyL^^HZyMtB:<J::s>xGyA:::::c]BC::yA::::::::Z:^H;Z:ji;yA:::::vQ<J:L
A<:y?xyy;::::::::::::::::::::::::::::::::ri>:J:Bajisy::ri>Cc=ry^H<Z:>:
JH[Ymy;::::JtBL<:jy;::::::Ba>:K\\:vQryyanK:>Z:jyyEvY::::jYC:LA<:y?xyy;
::::::::::::::::::::::BW>Cxyi[y=::::::::::::::::::::::::::::::::::::::
:::::xE;:>:lCvUxI::xEKLt:xIc]:B:;:^MrqvY:::::^H\\^::vY:::JtB:>:::J^:ry
vU<J^^MrqvY::ZnK:<ZyyQry:::ZyL:^H>:xEvyy=:::::::::::::::::::::::J:vyyu
y:::::::::::::::::::::::::ZYM:\\^:jyyEvYxG;:^HxyyyEyA:::::::::::::::::
:::::;BWB:;Zn;ry:::KDaJ::::y?xyy;:::::c]B?:xGvY:::::::\\NH[::::JH[Ymy;
:::JHK:\\>;BLvYjy;:::::::K<<J::::Ba:xI:::::::::::::::::::J:LA>:LAxyYsy
:::K<>:::jY[yyY:::::JtBL;ZY=yA::::::::Z::<:y@vY:::::JHK:\\>;BLvYjy;:::
::::KDaB:;:::ZV<y`y=:::::::::::::::::::>Zn;;Zn[yyQxI::J^:;:::vQryyA:::
::^H\\N:rqjy;::::::B:Z:ji;yanK:<Z:JH[Ymy;:::JH[BK:\\>yAvY:::::::J^lC<J
::::Ba:xI:::::::::::::::::::::::::::::::::::::::::::::::::::::::J:LA>:
LAxyYsy:::K<>:::jY[yyY:::::JtBL;ZY=yA:::ZB_MB:::ZY=xIBWvuV@CvY::JHK:\\
>;ryy?xI:::Ba:>CxyiwYxI:::::::BLJ:<::::s>vYyA::::::::::;jyyyyyI:::::::
:::::::::::::::::::BW>:;B::vyy<LqYyyyyEyA::::::::::::::::::::::s>\\>;B
LvyY=yA:jYsyy`:>CB::Zn[yyQxI:::::::::::::::Jtxe:>Z:>:::J^ji[y=:::J^:;Z
y<yyy::::::::ZnK:B:::ZB;jy;:::::::::::::::::::s>\\>;:yAvY::y_yyU<J^Z::
:LAxyYsy::::::::::::::BLJ:<::::BLrqjy;::::K<>:xEvyy=::::::::LA;B:<:::B
L:vY:::::::::::::::::::JH[BK:jy;yA:jYsyy`:>CB::Zn[yyQxI::::::::::::::j
YC:;BW>Z:jyyEvYLA;J:<:c]yyyyly;:::J^:;Zy<yyy::::::::ZnK:B:::ZB[Y=yA:::
::::::::::::::::::::::::::::::::::::::::::::::::::::^MBL>:vYjy;:vQxyiC
:K<<::BWryy_y=::::::::::::>Cxe:jyyI:s^y`hB[y=LAyHaK<yA:ZyxY;B:c]:>:xyY
wYxI:::BL>:;B:vQryyA::::::::^H<:;:::>CvUyay=:::::::::J:vyyyyy=::::::::
::::::::::::::::::::::::::::::::::::::::::::::<JtJ:<:y@vY::rqyqyK^:;:^
MrqvY::::::::::::::::ZB;<:::rqZy=:::xG;BLJ^ji[y=::::::::J^:;:::vUjy;::
:::::::::::::::::B:c=<:y@vY::rqvY>CJ::s>jy;::::::::::::::\\>B::::ZB;jy
;:::rq>ZB;:ry:::::::::>CJ::::y@vY::::::::::::::::::::<JtZ:ji;yA::xGyAK
<>:JH;vY:::::::::::::::vQ<J:LA\\>:yanK:>Z:JtryyyivY:::ZYM:\\>>CvUry:::
::::::>CJ::::y@vY:::::::::::::::::::::::::::::::::::::::::::::::::::::
:::<JtZ:ji;yA::xGyAK<>:JH[Ymy;:::::::::::::<:yO:ryyA::ZnkimS^jy;:yxy<J
^Z::xyYwYxI:::y`::\\>xgymy;::::::::BLZ::::xGry::::::::::>Z:vyyyyy=::::
::::::::::::::::::::::::::::::::::::::::::::::::::lC;J^B:s>xGyA:::::::
:::::::::::::::::K\\yD:vyy=JHsicELry:::ZnK:>Z:jyyeymy;:::::::::BLJ:ryy
AZV<K<yA:::::::::::::::::::ZVL:>C^MrqvY:::::::::::::::::::::ZyxYcE:cmy
yEyAB:cM:>Z:ji;yA::::ZnwQ;B:<:yayuyyA:::::::::ZB;;ryxyy;Bavqn?CvY:::::
:::::::::::::::lC;J^JH[Ymy;:::::::::::::::::::::jYyi:BW>Z:jysyvY<JtJ:<
:y?xyy;:::BW>Z:B:vYjy;:::::::::BLJ:ryyAZVlYMQ^jy;:::::::::::::::::::::
::::::::::::::::::::::::::::::::::Ba>:K<s>xGyA::::::::::::::::::::rq>Z
BsijyyI::BWvuV@CvY:xwy?:<:;:Zymysy:::^H<J:<J:ryZy=:::::::::J^Z:jyyI:s^
yDLry::::::::::>:yyyxI::::::::::::::::::::::::::::::::::::::::::::::::
:::::::K\\:B:;ZyyQyay=::::::::::::::::::::::::<JtvQ;:yA:::::vU<J^ZY=xI
:::::::::::;BW:xI:::::::::::::::::::::::K<>:xIyay=::::::::::::::::::::
:JtBaKD:vUxI<:;Z:jisyvY::::jiC:K<:xI:::::::::::;BWxe:jyyI:::::::::::::
::::::::::K<>:xIyay=:::::::::::::::::::::jiC:K<<:y@^mYE:;BLBLvyYuyvY::
:jiC:K<xGry:::::::::::>Zn[:Zy=::::::::::::::::::::::::::::::::::::::::
::::::::::::::::::J^Z:>:xyYwYxI:::::::::::::::::::::s>;BLy@vY::LAyHaK<
yAZ:^H;J:<:BL;J^LAy?xI::rqyQ:\\>vUjy;::::::::::B:cmY?:xyy;::::::::::::
;B:yyyxI:::::::::::::::::::::::::::::::::::::::::::::::::::::::B:cM:>Z
V<y`y=:::::::::::::::::::::::ZYM:\\^y<yyy:::::>Zn;y@vY:::::::::::jiC:K
<jy;::::::::::::::::::::::B:c=lCvUxI::::::::::::::::::::::\\>yHajyC:Z:
ji;yA::::>::jy;:::::::::::y`:>CZyyY:::::::::::::::::::::::<JtZV<y`y=::
:::::::::::::::::::ZBK:B:::^HxiyxYyA::::;:vUjy;:::::::::::y`:>CZyyY:::
::::::::::::::::::::::::::::::::::::::::::::::::::::::::<JtZV<y`y=::::
::::::::::::::::Z::xyYwYxI:BWBajy;K<>::xIKDayxyyGWyay=::<:rqZy=:::::::
::::xwy?ZB;vyy=:::::::::::J:<jyyiy=:::::::::::::::::::::::::::::::::::
::::::::::::::::::::J:LA<jY;yA::::::::::::::::::::::::^M<J:\\ni;yA:::v
U<J^>:xyY[y=::::::::::::lC<:Zy=::::::::::::::::::::::J:LA<jY;yA:::::::
::::::::::::::ZYM:\\^yyqn;c=<:y@vY:::jiC:KL:ryZy=::::::::::::lC<J^:xI:
::::::::::::::::::::::;BWB:y?vY::::::::::::::::::::::lC<J^<Z:^HvyyxYyA
:::::y`:>Cryy?xI::::::::::::BaB:xGry::::::::::::::::::::::::::::::::::
:::::::::::::::::::::::::>Zn[:vQryyA::::::::::::::::::::ZBK:BWryy_y=Zn
kimCvYLA;B:<::y@>CxyYMAxI:rqyQ:\\>vyy<yA::::::::::::^M<J:\\>jy;:::::::
::::;jyyyyyI::::::::::::::::::::::::::::::::::::::::::::::::::::::::BW
>:;Bajisy::::::::::::::::::::::::B:c=xyY[y=::J:ri<:yyy::ZyxY;B:c]:>:J^
<ZyyUyay=::::::J:La:B:yyixIyA::::::::::::::::::::::ZnK:<ZV<y`y=:::::::
::::::::::::::vQLQ:LAyG:c=<:y@vY:::J:LayD:yqyyI::riyQ:<JtJ::K<y@xI::::
:::;BW<Z:vyytyxyy;::::::::::::::::::::::BWyO:<ZV<y`y=:::::::::::::::::
::::>C<:;ZY=xI:::::;BWxe:jyyI::ri>Z:^H>:J^ji[y=::::::J:La:B:yyixIyA:::
:::::::::::::::::::::::::::::::::::::::::::::::::::::::ZnK:<ZV<y`y=:::
::::::::::::::::ZnK:B:vUjy;BWvuV@CZ:J::rqZyM^ryyGWry:Z:^HyO:ryyA::vqyE
:;BWB:ZB[YuyvY:::::::<Jt>:;ryyoysy:::::::::::>Z:vyyuy:::::::::::::::::
::::::::::::::::::::::::::::::::::::::::Z:^HyO:jy;::::::::::::::::::::
:::BL>:;BWvYy_y=::::::Z:J:B:vQryyxy<J^vuV<yA::::::>C<:c=xEyA::::::::::
:::::::::::::B:cmY[yyY::::::::::::::::::::::LAsFL;B:cEaB:vUxIyA:::::::
Z:J:B:vQryy`:>ClCvY::::::J^B:^h:Zyly;:::::::::::::::::::::::<JtvQryyA:
::::::::::::::::::::vU<J^>:\\>yyqjy;::::::::B:cM:B:vQjiC:KlimCvY::::::
J^B:^Hvyyly;::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
:<JtvQryyA::::::::::::::::Zn[y`hymy;BLZ:JHsyxGyABWBaKDaxY:<J^B:;:vQryy
A>CvQry::::::>ZnC:<J:riZYyY;BL^Myay=::::::\\>;Zn;ywyxI::::::::::J:<jyw
yy=:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
::::::::::::::::LA;J:<:y@vY:::::::\\>:ryZVxU;J^xyYMAxI::::::c=<J:rqZy=
:::::::::::::::::::::::::::::::::::::::::::::::J^:;:vUjy;:::::::BL:Zy=
lC>CZy=:::::JtZ:>:xGry:::::::::::::::::::::::::::::::::::::::::::::::Z
YM:\\^:J:ryy?xI::::::::BLZY=xIBaB:K<ry::::::^HB:;ZY=xI::::::::::::::::
::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::ri>c:^Hy
pysy^HJ::s>xGyABW^mV@C;BW>Z::lCyqisy:KDaxyYMAxI::::::K\\:ji;yA^mYE:\\>
jy;:::::BW>:;B:vUjy;::::::::::;jyyyyyI::::::::::::::::::::::::::::::::
::::::::::::::::::::::::::::::::::::::::::::::::BWrijy;BLJ:<:s>xGyA:::
::::::BaJ^lS^:xI::Jtryy?xI:K<<J:Bajisy::::::::::::::::::::::::::::::::
::::::::::::::::y`:>C;Z:ji;yA::::::::::ZV\\:>CK<ry:::c]yyQry:>CB:;ZV<y
`y=:::::::::::::::::::::::::::::::::::::::::::::::ZB;<:ryy?xI:::::::::
:BaJ^:ry:::c]yyQry:>CB:;ZV<y`y=:::::::::::::::::::::::::::::::::::::::
:::::::::::::::::::::::::::::::::::::::>CJ::::y?xyy;BW>:<::c]yyyyxYyA:
K\\yyqn[y=::::::::JHC:\\>rqvY::ZnkyyEvY:\\>;J:<:s>xGyA::::::::::;jywyy
=:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
:::::::::::xuy?c::ry^H<Z:>:JH[Ymy;:::::::::\\NH[n;y_y=::vQ\\N::vYLA;Z:
:lCvUxI::::::::::::::::::::::::::::::::::::::::::::::::xE;JtB:y@vY::::
:::::::\\NHK:LAyqYsy:::y_B?::yanK:B:ZV<y`y=:::::::::::::::::::::::::::
:::::::::::::::::::::ZnK:B:>c:ryy@xI:::::::::BLs>LAxyYsy:::y_B?::yanK:
B:ZV<y`y=:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
:::::::::::::::::vU<J^>:<::BWjYsy:B:c=<:BLrqjy;rq>ZBCajisy:::::::::KDa
JtjyyEyA::ri>c::ry^H<J:>:JH[Ymy;:::::::::J:vYyyy::::::::::::::::::::::
:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::>cV\\:>:::j
Y;yA:::::::::^MBL>Zn;y_y=::ZB;;B:::Zy<yyy:::::::::::::::::::::::::::::
::::::::::::::::::::^MBLy@vY::::::::::JH;;Zn;y_y=::ZB;;B:::Zy<yyy:::::
:::::::::::::::::::::::::::::::::::::::::::::::::::::::::^MBLBWjYsy:::
BLJ:<:::rijyyI::::::::::::::::::::::::::::::::::::::::::::::::::::::::
::::::::::::::::::::::::K<>:JH[Ymy;<JtZ:::xyY[y=J::;:ZY=xI:::::::BaB:K
<c=yyivY:::>CB:;:::vQryyA::::::::::>:yay=:::::::::::::::::::::::::::::
:::::::::::::::::::::::::::::::::::::::::::::::::::jiC:KL:B::Zn;y_y=::
::::::ZB;;B:Zy<yyy:::ZYM::;::^HrivY:::::::::::::::::::::::::::::::::::
::::::::::::::::::::::::::ZB;<:rijyyI:::rq>:J:::c=xEyA::::::::::::::::
:::::::::::::::::::::::::::::::::::::::::::::BLZ::xEvyy=:::xG;:>::JtZy
ly;:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
:::::::::::::::::::::::::::::::::J^:;:vQryyA:::vU<:B::Zn;y_y=:::::::::
:>Z:vYyyy:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
:::::::::::::::::::::>CB:;:^MrqvY::::::::ZyL:^H<J::y?xyy;::::BLJ:<:Baj
isy:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::ri>:c=
;:vQryyA::::ZB;;B:ZV<y`y=:::::::::::::::::::::::::::::::::::::::::::::
:::::::::::::::ZyL:^H>:jY[yyY:::::\\>>Z::lCvUxI:::::::::::::::::::::::
::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
:::::::jYC:LA<:rijyyI:::::K<<J::s>xGyA:::::::::::;jywyy=::::::::::::::
::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
:::::::::::LA;J:LAyqYsy:::::::::::::::::::::::::::::::::::::::::::::::
::::::::::::::::::::::::BW>::y_y=:::::::::::::::::::::::::::::::::::::
:::::::::::::::::::::::::::::::::ZnK::vQxI::::::::::::::::::::::::::::
::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
::::::::::::JtB::xEyA::::::::::::::::::::;jywyy=::::::::::::::::::::::
::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
:xwiyiyyuyuy:K<<:rivY:::::::::::::::::::::::::::::::::::::::::::::::::
:::::::::::::::::::ZYyUxyiyiy=>C::yA::::::::::::::::::::::::::::::::::
::::::::::::::::::::::::::::::::::rqy`yyuyuy:K<:jy;:::::::::::::::::::
::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
::::::::::::::::::jiyGyyqyqy;\\>:Zy=:::::::::::::::::::>:yqyyI::::::::
::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
:::::::::::::::ri^mB_hyyyYmyyG;BLJ:ryy?yyy::::::::::::::::::::::::::::
::::::::::::::::::::::::::::::::::::::::ZyLH[YmyyG;:>:xIvyy=::::::::::
::::::::::::::::::::::::::::::::::::::::::::::::::::::::::xEs>xGyyq>:J
:ryjyyI:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
:::::::::::::::::::::::::::::::::::::::::::::y_V<y`yyU<:B:vYryyA::::::
:::::::::::::>Z:ryxI::::::::::::::::::::::::::::::::::::::::::::::::::
::::::::::::::::::::::::::::::::::::::::::::c]:B:;::^HrivY::::::::::::
:::::::::::::::::::::::::::::::::::::::::::::::::::::::::^H<:;::^HrivY
:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::^
H<:;::^HrivY::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
::::::::::::::::::::::::::::::::::::::::::::::::::ZnK:B::Zn;y_y=::::::
:::::::::::::>:yqyyI::::::::::::::::::::::::::::::::::::::::::::::::::
::::::::::::::::::::::::::::::::::::::::::::ri>:c]:>:LAyqYsy::::::::::
::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::ri>:B:;Znk
y[y=::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
:::ZyL:Z:>:LAyAxI:::::::::::::::::::::::::::::::::::::::::::::::::::::
::::::::::::::::::::::::::::::::::::::::::::::::::::::::jYC:J:<:c]y=yA
::::::::::::::::::::;jywyy=:::::::::::::::::::::::::::::::::::::::::::
::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
::::::::::::::::::::::::::::::::::::::::::::::::::::::::J:Zy=:::::::::
::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
::::::::::::::::::::J:Zy=:::::::::::::::::::::::::::::::::::::::::::::
::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
::::::::::::::::::::::::::::::::::::::::::::::::::::::J:Zy=:::::::::::
::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
::::::::::::::::::J:Zy=:::::::::::::::::::::::::::::::::::::::::::::::
::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
::::::::::::::::::::::::::::::::::::::::::::::::::::J:Zy=:::::::::::::
::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
::::::::::::::::J:Zy=:::::::::::::::::::::::::::::::::::::::::::::::::
::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
::::::::::::::::::::::::::::::::::::::::::::::::::J:Zy=:::::::::::::::
::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
::::::::::::::J:Zy=:::::::::::::::::::::::::::::::::::::::::::::::::::
::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
::::::::::::::::::::::::::::::::::::::::::::::::J:Zy=:::::::::::::::::
::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
::::::::::::J:Zy=:::::::::::::::::::::::::::::::::::::::::::::::::::::
::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
::::::::::::::::::::::::::::::::::::::::::::::J:Zy=:::::::::::::::::::
::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
::::::::::J:Zy=:::::::::::::::::::::::::::::::::::::::::::::::::::::::
::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
::::::::::::::::::::::::::::::::::::::::::::J:Zy=:::::::::::::::::::::
::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
::::::::J:Zy=:::::::::::::::::::::::::::::::::::::::::::::::::::::::::
::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
::::::::::::::::::::::::::::::::::::::::::J:Zy=:::::::::::::::::::::::
::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
::::::J:Zy=:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
::::::::::::::::::::::::::::::::::::::::J:Zy=:::::::::::::::::::::::::
::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
::::J:Zy=:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
::::::::::::::::::::::::::::::::::::::J:Zy=:::::::::::::::::::::::::::
::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
::J:Zy=:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
::::::::::::::::::::::::::::::::::::J:Zy=:::::::::::::::::::::::::::::
::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
J:Zy=:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
::::::::::::::::::::::::::::::::::J:>Z::::::::::::::::::::::::::=ja:>:
::::::::J?<J;<jyyiy=J:B::::::VZ:>:cB:<J:::::::::::::yay=J:B:::::::::::
::::::::jysy:>:<:::::::::::::::::::vYxI:;Z:::::::::2:" }}{PARA 0 "" 0 
"" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 569 0 "" }{TEXT 559 34 "is a \+
right Riemann sum.  What is  " }{XPPEDIT 570 0 "limit(S[N],N = infinit
y);" "6#-%&limitG6$&%\"SG6#%\"NG/F)%)infinityG" }{TEXT 558 2 " ?" }
{TEXT 571 1 " " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" 
{TEXT 608 75 "a)  16            b)  20             c)   24           d
)  32            e)" }{TEXT 611 1 " " }{TEXT 612 3 " 36" }{TEXT 613 1 
" " }{TEXT 610 1 " " }{TEXT 609 17 "                 " }}{PARA 0 "" 0 
"" {TEXT 607 81 "f)   44           g)   56             h)   60        \+
   i)  64             j)  72" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 
0 "" 0 "" {TEXT -1 0 "" }}{PARA 3 "" 0 "" {TEXT 567 8 "Solution" }
{TEXT 568 8 ": ( h )\n" }{TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 24 "
A right Riemann sum of  " }{XPPEDIT 18 0 "f(x);" "6#-%\"fG6#%\"xG" }
{TEXT -1 37 "  on the interval [a,b] has the form " }}{PARA 0 "" 0 "" 
{TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 
"" {MPLTEXT 1 0 8 "restart:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
73 "f(a+(b-a)/N)*(b-a)/N+f(a+2*(b-a)/N)*(b-a)/N+`...`+f(a+N*(b-a)/N)*(
b-a)/N;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,**(-%\"fG6#,&%\"aG\"\"\"*&
,&%\"bGF*F)!\"\"F*%\"NGF.F*F*F,F*F/F.F**(-F&6#,&F)F**(\"\"#F*F,F*F/F.F
*F*F,F*F/F.F*%$...GF**(-F&6#F-F*F,F*F/F.F*" }}}{PARA 0 "" 0 "" {TEXT 
-1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 45 "Comparing this with the given s
um we see that" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 
0 "" {MPLTEXT 1 0 54 "a := 2;\nDelta := 2/N;\nb := a + N*Delta;\nf := \+
x -> x^3;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"aG\"\"#" }}{PARA 11 "
" 1 "" {XPPMATH 20 "6#>%&DeltaG,$*&\"\"#\"\"\"%\"NG!\"\"F(" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6#>%\"bG\"\"%" }}{PARA 11 "" 1 "" {XPPMATH 20 
"6#>%\"fGf*6#%\"xG6\"6$%)operatorG%&arrowGF(*$)9$\"\"$\"\"\"F(F(F(" }}
}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 64 "Since th
e limit of the Riemann sums is the Riemann integral of  " }{XPPEDIT 
18 0 "f;" "6#%\"fG" }{TEXT -1 21 " over [a,b], we have:" }}{PARA 0 "" 
0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 56 "Answer \+
:= Int(f(x), x = a .. b);\nanswer = value(Answer);" }}{PARA 11 "" 1 "
" {XPPMATH 20 "6#>%'AnswerG-%$IntG6$*$)%\"xG\"\"$\"\"\"/F*;\"\"#\"\"%
" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/%'answerG\"#g" }}}{PARA 0 "" 0 "
" {TEXT -1 0 "" }}}{SECT 0 {PARA 3 "" 0 "" {TEXT 376 15 "3. Calculate \+
  " }{XPPEDIT 380 0 "int(sec(theta)^2,theta = 0 .. Pi/3);" "6#-%$intG6
$*$-%$secG6#%&thetaG\"\"#/F*;\"\"!*&%#PiG\"\"\"\"\"$!\"\"" }{TEXT 379 
1 "." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" 
}}{PARA 0 "" 0 "" {TEXT 382 28 "a)    1                  b) " }
{XPPEDIT 261 0 "sqrt(2);" "6#-%%sqrtG6#\"\"#" }{TEXT 383 20 "         \+
       c)  " }{XPPEDIT 262 0 "sqrt(3);" "6#-%%sqrtG6#\"\"$" }{TEXT 
384 16 "             d) " }{XPPEDIT 256 0 "sqrt(2)-1;" "6#,&-%%sqrtG6#
\"\"#\"\"\"F(!\"\"" }{TEXT 543 25 "                     e)  " }
{XPPEDIT 263 0 "sqrt(3)-1;" "6#,&-%%sqrtG6#\"\"$\"\"\"F(!\"\"" }{TEXT 
385 9 "  \nf)    " }{XPPEDIT 264 0 "sqrt(3)/2;" "6#*&-%%sqrtG6#\"\"$\"
\"\"\"\"#!\"\"" }{TEXT 386 18 "              g)  " }{TEXT 393 1 " " }
{XPPEDIT 265 0 "sqrt(2)/2;" "6#*&-%%sqrtG6#\"\"#\"\"\"F'!\"\"" }{TEXT 
387 18 "              h)  " }{XPPEDIT 266 0 "2*sqrt(3);" "6#*&\"\"#\"
\"\"-%%sqrtG6#\"\"$F%" }{TEXT 388 13 "          i) " }{TEXT 391 1 " " 
}{XPPEDIT 267 0 "3*sqrt(2);" "6#*&\"\"$\"\"\"-%%sqrtG6#\"\"#F%" }
{TEXT 389 2 "  " }{TEXT 392 26 "                      j)  " }{XPPEDIT 
268 0 "3*sqrt(3);" "6#*&\"\"$\"\"\"-%%sqrtG6#F$F%" }{TEXT 381 1 "\n" }
{TEXT 390 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" 
{TEXT -1 0 "" }}{PARA 3 "" 0 "" {TEXT 394 8 "Solution" }{TEXT 395 8 ":
 ( c )\n" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 
0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 47 "indefiniteIntegral :=
 Int(sec(theta)^2, theta);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%3indef
initeIntegralG-%$IntG6$*$)-%$secG6#%&thetaG\"\"#\"\"\"F-" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 59 "indefiniteIntegralEvaluated := valu
e( indefiniteIntegral );" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%<indefin
iteIntegralEvaluatedG*&-%$sinG6#%&thetaG\"\"\"-%$cosGF(!\"\"" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 99 "answer := subs(theta=Pi/3, i
ndefiniteIntegralEvaluated)-subs(theta=0, indefiniteIntegralEvaluated)
;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%'answerG,&*&-%$sinG6#,$*&\"\"$!
\"\"%#PiG\"\"\"F/F/-%$cosGF)F-F/*&-F(6#\"\"!F/-F1F4F-F-" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 37 "simplifiedAnswer := simplify(answer
);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%1simplifiedAnswerG*$\"\"$#\"\"
\"\"\"#" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 
0 "" }}}{SECT 0 {PARA 260 "" 0 "" {TEXT 262 3 "4. " }{TEXT 317 1 " " }
{TEXT 359 17 "  Suppose that   " }{XPPEDIT 18 0 "f(x) = (4*x^2+4*x+20)
/(x^2+x);" "6#/-%\"fG6#%\"xG*&,(*&\"\"%\"\"\"*$F'\"\"#F,F,*&F+F,F'F,F,
\"#?F,F,,&*$F'F.F,F'F,!\"\"" }{TEXT 358 1 " " }{TEXT 475 1 "." }{TEXT 
476 16 "     What is    " }{XPPEDIT 18 0 "int(D(f)(x),x = 1 .. 4);" "6
#-%$intG6$--%\"DG6#%\"fG6#%\"xG/F,;\"\"\"\"\"%" }{TEXT 360 3 "  ?" }}
{PARA 3 "" 0 "" {TEXT 316 183 "a)   - 9           b) - 7             c
)  - 5            d)  - 3            e)   - 1         \nf)  1         \+
      g)   3             h)    5             i)   7               j)  \+
   9 " }{TEXT 318 7 "      \n" }}{PARA 3 "" 0 "" {TEXT 319 8 "Solution
" }{TEXT 320 6 ": (a)\n" }{TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 8 "restart;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 33 
"f := x -> (4*x^2+4*x+20)/(x^2+x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#
>%\"fGf*6#%\"xG6\"6$%)operatorG%&arrowGF(*&,(*&\"\"%\"\"\")9$\"\"#F0F0
*&F/F0F2F0F0\"#?F0F0,&*$F1F0F0F2F0!\"\"F(F(F(" }}}{EXCHG {PARA 0 "> " 
0 "" {MPLTEXT 1 0 64 "answer := f(4) - f(1);  #Fundamental Theorem of \+
Calculus, Part I" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%'answerG!\"*" }}
}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}
{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}
{SECT 0 {PARA 3 "" 0 "" {TEXT 440 16 "5. Suppose that " }{XPPEDIT 441 
0 "int(2*f(x),x = 1 .. 4) = 5;" "6#/-%$intG6$*&\"\"#\"\"\"-%\"fG6#%\"x
GF)/F-;F)\"\"%\"\"&" }{TEXT 442 5 " ,   " }{XPPEDIT 573 0 "int(f(x),x \+
= -1 .. 1) = 9/2;" "6#/-%$intG6$-%\"fG6#%\"xG/F*;,$\"\"\"!\"\"F.*&\"\"
*F.\"\"#F/" }{TEXT 572 10 " ,   and  " }{XPPEDIT 443 0 "int(`(`*c+f(x)
*`)`,x = -1 .. 4) = 22;" "6#/-%$intG6$,&*&%\"(G\"\"\"%\"cGF*F**&-%\"fG
6#%\"xGF*%\")GF*F*/F0;,$F*!\"\"\"\"%\"#A" }{TEXT 444 18 ".    What is \+
  c ?" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 448 66 
"a)  1           b)  2             c)   3        d)  4           e)" }
{TEXT 451 2 "  " }{TEXT 445 1 "5" }{TEXT 450 2 "  " }{TEXT 449 19 "   \+
                " }}{PARA 0 "" 0 "" {TEXT 446 33 "f)   6           g) \+
  7          " }{TEXT -1 1 " " }{TEXT 447 38 "h)   8         i)  9    \+
        j)  10" }{TEXT -1 3 "   " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}
{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 3 "" 0 "" {TEXT 452 8 "Solution
" }{TEXT 453 8 ": ( c )\n" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "
restart;" }}}{EXCHG {PARA 0 "> " 0 "" {XPPEDIT 19 1 "eqn1 := int(c+f(x
),x = -1 .. 4) = 22;   " "6#>%%eqn1G/-%$intG6$,&%\"cG\"\"\"-%\"fG6#%\"
xGF+/F/;,$F+!\"\"\"\"%\"#A" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%eqn1G
/-%$intG6$,&%\"cG\"\"\"-%\"fG6#%\"xGF+/F/;!\"\"\"\"%\"#A" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "eqn2 := c = solve(eqn1, c);" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%eqn2G/%\"cG,&*&#\"\"\"\"\"&F*-%$int
G6$-%\"fG6#%\"xG/F2;!\"\"\"\"%F*F5#\"#AF+F*" }}}{EXCHG {PARA 0 "> " 0 
"" {MPLTEXT 1 0 95 "eqn3 := subs(int(f(x),x = -1 .. 4) = int(f(x),x = \+
-1 .. 1)+(1/2)*int(2*f(x),x = 1 .. 4), eqn2);" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>%%eqn3G/%\"cG,(*&#\"\"\"\"\"&F*-%$intG6$-%\"fG6#%\"xG/
F2;!\"\"F*F*F5*&#F*\"#5F*-F-6$,$*&\"\"#F*F/F*F*/F2;F*\"\"%F*F5#\"#AF+F
*" }}}{EXCHG {PARA 0 "> " 0 "" {XPPEDIT 19 1 "subs( \{int(f(x),x = -1 \+
.. 1) = 9/2, int(2*f(x),x = 1 .. 4)=5\}, eqn3);" "6#-%%subsG6$<$/-%$in
tG6$-%\"fG6#%\"xG/F.;,$\"\"\"!\"\"F2*&\"\"*F2\"\"#F3/-F)6$*&F6F2-F,6#F
.F2/F.;F2\"\"%\"\"&%%eqn3G" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/%\"cG\"
\"$" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" 
}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{SECT 0 {PARA 3 "" 0 "" {TEXT 415 
17 "6. Suppose that  " }{XPPEDIT 416 0 "f(x) = 3*x^2-2*x;" "6#/-%\"fG6
#%\"xG,&*&\"\"$\"\"\"*$F'\"\"#F+F+*&F-F+F'F+!\"\"" }{TEXT 417 72 " .  \+
The Mean Value Theorem for Integrals asserts that there is a point  " 
}{XPPEDIT 418 0 "c;" "6#%\"cG" }{TEXT 419 38 "  in the interval   [1,4
]  such that  " }{XPPEDIT 420 0 "f(c) = f[ave];" "6#/-%\"fG6#%\"cG&F%6
#%$aveG" }{TEXT 421 10 "   where  " }{XPPEDIT 422 0 "f[ave];" "6#&%\"f
G6#%$aveG" }{TEXT 423 27 "  is the average value of  " }{XPPEDIT 424 
0 "f(x);" "6#-%\"fG6#%\"xG" }{TEXT 425 6 "  for " }{XPPEDIT 426 0 "x;
" "6#%\"xG" }{TEXT 427 34 " in  the interval [1,4]. What is  " }
{XPPEDIT 428 0 "c;" "6#%\"cG" }{TEXT 429 1 "?" }}{PARA 0 "" 0 "" 
{TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 432 1 "\n" }{TEXT 433 85 "a)  4/
3               b)  5/3            c)   2            d)  7/3          \+
 e)  8/3 " }{TEXT 435 2 "  " }{TEXT 434 20 "                   \n" }
{TEXT 430 41 "f)  3                  g)  10/3          " }{TEXT 436 1 
" " }{TEXT 431 37 "h) 11/3        i)   5/2           j) " }{TEXT 437 
4 " 7/2" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 
"" }}{PARA 3 "" 0 "" {TEXT 438 8 "Solution" }{TEXT 439 8 ": ( e )\n" }
}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 36 "a := 1;\nb := 4;\nf := x -> 3*x^2-2*x;" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>%\"aG\"\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"bG
\"\"%" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"fGf*6#%\"xG6\"6$%)operato
rG%&arrowGF(,&*&\"\"$\"\"\")9$\"\"#F/F/*&F2F/F1F/!\"\"F(F(F(" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "m := Int(f(x),x=1..4)/(b-a);
" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"mG,$*&#\"\"\"\"\"$F(-%$IntG6$,
&*&F)F()%\"xG\"\"#F(F(*&F1F(F0F(!\"\"/F0;F(\"\"%F(F(" }}}{EXCHG {PARA 
0 "> " 0 "" {MPLTEXT 1 0 14 "m := value(m);" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>%\"mG\"#;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
19 "solve(f(c) = m, c);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$#\"\")\"\"$
!\"#" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "
" }}{PARA 0 "" 0 "" {TEXT -1 43 "Only the first solution is in the int
erval." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{SECT 0 {PARA 3 "" 0 "" 
{TEXT 323 19 "7.  Calculate      " }{XPPEDIT 363 0 "`d `/(d*x);" "6#*&
%#d~G\"\"\"*&%\"dGF%%\"xGF%!\"\"" }{TEXT 362 1 " " }{XPPEDIT 257 0 "in
t((7*t+22)/(t^3+4),t = 0 .. x);" "6#-%$intG6$*&,&*&\"\"(\"\"\"%\"tGF*F
*\"#AF*F*,&*$F+\"\"$F*\"\"%F*!\"\"/F+;\"\"!%\"xG" }{TEXT 361 11 "     \+
at    " }{XPPEDIT 365 0 "x = 2;" "6#/%\"xG\"\"#" }{TEXT 364 1 "." }}
{PARA 3 "" 0 "" {TEXT 322 1 "\n" }}{PARA 3 "" 0 "" {TEXT 321 133 "a) 0
            b)  1          c)  2         d)  3          e)  4  \nf)   \+
6          g)   9         h)  12        i)  16        j)  18" }{TEXT 
556 1 "\n" }}{PARA 3 "" 0 "" {TEXT 324 8 "Solution" }{TEXT 325 8 ": ( \+
d )\n" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "f := t -> (7*t+22)/
(t^3+4);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"fGf*6#%\"tG6\"6$%)oper
atorG%&arrowGF(*&,&*&\"\"(\"\"\"9$F0F0\"#AF0F0,&*$)F1\"\"$F0F0\"\"%F0!
\"\"F(F(F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "Answer := sub
s(t=2, f(t)); \n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%'AnswerG\"\"$" }
}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{SECT 0 {PARA 3 "" 0 "" {TEXT 370 
17 "8. Suppose that  " }{XPPEDIT 257 0 "F(x) = int(sqrt(t^2+20),t = 0 \+
.. ` `*x^2);" "6#/-%\"FG6#%\"xG-%$intG6$-%%sqrtG6#,&*$%\"tG\"\"#\"\"\"
\"#?F2/F0;\"\"!*&%\"~GF2*$F'F1F2" }{TEXT 371 15 ".    What is   " }
{XPPEDIT 373 0 "D(F)(2);" "6#--%\"DG6#%\"FG6#\"\"#" }{TEXT 372 3 "?  \+
" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}
{PARA 0 "" 0 "" {TEXT 575 75 "a)  16            b)  20             c) \+
  24           d)  32            e)" }{TEXT 578 1 " " }{TEXT 579 3 " 3
6" }{TEXT 580 1 " " }{TEXT 577 1 " " }{TEXT 576 17 "                 \+
" }}{PARA 0 "" 0 "" {TEXT 574 81 "f)   44           g)   48           \+
  h)   60           i)  64             j)  72" }}{PARA 0 "" 0 "" 
{TEXT -1 1 " " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" 
{TEXT -1 0 "" }}{PARA 256 "" 0 "" {TEXT 374 8 "Solution" }{TEXT 375 7 
": ( c )" }{TEXT -1 1 "\n" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 43 
"F := (x) -> Int(sqrt(t^2+20),t = 0 .. x^2);" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>%\"FGf*6#%\"xG6\"6$%)operatorG%&arrowGF(-%$IntG6$-%%sq
rtG6#,&*$)%\"tG\"\"#\"\"\"F7\"#?F7/F5;\"\"!*$)9$F6F7F(F(F(" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "D(F)(x);" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#,$*(\"\"#\"\"\"%\"xGF&,&*$)F'\"\"%F&F&\"#?F&#F&F%F&" }}
}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "D(F)(2);" }}{PARA 11 "" 1 "
" {XPPMATH 20 "6#,$*&\"\"%\"\"\"\"#O#F&\"\"#F&" }}}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 20 "simplify( D(F)(2) );" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#\"#C" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{SECT 0 
{PARA 3 "" 0 "" {TEXT 260 1 " " }{TEXT 369 1 "9" }{TEXT -1 2 ". " }
{TEXT 366 14 "Suppose that  " }{XPPEDIT 367 0 "F(x) = int(sqrt(1/2+t^2
),t = ` `*cos(x) .. ` `*sin(x));" "6#/-%\"FG6#%\"xG-%$intG6$-%%sqrtG6#
,&*&\"\"\"F0\"\"#!\"\"F0*$%\"tGF1F0/F4;*&%\"~GF0-%$cosG6#F'F0*&F8F0-%$
sinG6#F'F0" }{TEXT 368 14 ".    What is  " }{XPPEDIT 582 0 "D(F)(Pi/4)
;" "6#--%\"DG6#%\"FG6#*&%#PiG\"\"\"\"\"%!\"\"" }{TEXT 581 3 " ? " }
{TEXT -1 1 " " }}{PARA 0 "" 0 "" {TEXT -1 1 " " }}{PARA 0 "" 0 "" 
{TEXT -1 0 "" }}{PARA 3 "" 0 "" {TEXT 396 109 "a)  0           b)   1/
2             c)  1               d)    2              e)   3  \nf)  4
            g)   " }{XPPEDIT 586 0 "sqrt(2);" "6#-%%sqrtG6#\"\"#" }
{TEXT 583 16 "            h)  " }{XPPEDIT 587 0 "2*sqrt(2);" "6#*&\"\"
#\"\"\"-%%sqrtG6#F$F%" }{TEXT 585 13 "         i)  " }{XPPEDIT 588 0 "
sqrt(2)/2;" "6#*&-%%sqrtG6#\"\"#\"\"\"F'!\"\"" }{TEXT 584 18 "        \+
     j)   " }{XPPEDIT 589 0 "3*sqrt(2);" "6#*&\"\"$\"\"\"-%%sqrtG6#\"
\"#F%" }{TEXT 397 1 "\n" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 
0 "" {TEXT -1 0 "" }}{PARA 3 "" 0 "" {TEXT 336 8 "Solution" }{TEXT 
337 8 ": ( g )\n" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 14 "with(student):" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 85 "v := x -> sin(x);\nu := x -> cos(x);\nF := (x) -> Int
(sqrt(1/2+t^2), t = u(x) .. v(x));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#
>%\"vG%$sinG" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"uG%$cosG" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6#>%\"FGf*6#%\"xG6\"6$%)operatorG%&arrowGF(-%$
IntG6$-%%sqrtG6#,&#\"\"\"\"\"#F4*$)%\"tGF5F4F4/F8;-%\"uG6#9$-%\"vGF=F(
F(F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 112 "eqn := 'D(F)(x)' =
 subs(t = v(x), integrand(F(x)))*Diff(v(x), x) - subs(t = u(x), integr
and(F(x)))*Diff(u(x),x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$eqnG/--
%\"DG6#%\"FG6#%\"xG,&*&#\"\"\"\"\"#F0*&,&F1F0*&\"\"%F0)-%$sinGF+F1F0F0
F/-%%DiffG6$F7F,F0F0F0*&#F0F1F0*&,&F1F0*&F5F0)-%$cosGF+F1F0F0F/-F:6$FB
F,F0F0!\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 55 " answer = si
mplify( subs(x = Pi/4, value(rhs(eqn)) ) );" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#/%'answerG*$\"\"##\"\"\"F&" }}}{PARA 0 "" 0 "" {TEXT 
-1 0 "" }}}{SECT 0 {PARA 3 "" 0 "" {TEXT -1 1 " " }{TEXT 339 17 "10. C
alculate    " }{XPPEDIT 399 0 "int((sqrt(x)+1)^3/sqrt(x),x = 0 .. 4);
" "6#-%$intG6$*&,&-%%sqrtG6#%\"xG\"\"\"F,F,\"\"$-F)6#F+!\"\"/F+;\"\"!
\"\"%" }{TEXT 398 2 " ." }}{PARA 0 "" 0 "" {TEXT 338 17 "             \+
    " }}{PARA 0 "" 0 "" {TEXT 400 163 "a)  4               b)  8      \+
         c)  12            d)  16           e)  20  \nf)   24         \+
   g)   28            h)  32             i)  36            j)  " }
{TEXT 401 2 "40" }{TEXT 590 1 "\n" }{TEXT -1 0 "" }}{PARA 3 "" 0 "" 
{TEXT 340 8 "Solution" }{TEXT 341 8 ": ( j )\n" }}{EXCHG {PARA 0 "> " 
0 "" {MPLTEXT 1 0 8 "restart:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 50 "Integral := Int((sqrt(x)+1)^3/sqrt(x),x = 0 .. 4);" }}{PARA 11 "
" 1 "" {XPPMATH 20 "6#>%)IntegralG-%$IntG6$*&,&*$%\"xG#\"\"\"\"\"#F-F-
F-\"\"$F+#!\"\"F./F+;\"\"!\"\"%" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 24 "value(Integral); #Answer" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"
#S" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 32 "He
re are the substitution steps:" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}
{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
14 "with(student):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "subst
itution := u=sqrt(x)+1;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%-substitu
tionG/%\"uG,&*$%\"xG#\"\"\"\"\"#F+F+F+" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 59 "equivalentIntegral := changevar(substitution, Integra
l, u);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%3equivalentIntegralG-%$Int
G6$,$*&\"\"#\"\"\")%\"uG\"\"$F+F+/F-;F+,&*$\"\"%#F+F*F+F+F+" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 39 "simplify( value( equivalentI
ntegral ));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"#S" }}}{PARA 0 "" 0 "
" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{SECT 0 {PARA 3 "" 
0 "" {TEXT -1 1 " " }{TEXT 259 19 "11.   Calculate    " }{XPPEDIT 258 
0 "int(15*x*sqrt(x-2),x = 2 .. 3);" "6#-%$intG6$*(\"#:\"\"\"%\"xGF(-%%
sqrtG6#,&F)F(\"\"#!\"\"F(/F);F.\"\"$" }{TEXT 402 2 " ." }}{PARA 0 "" 
0 "" {TEXT 269 6 " a)   " }{XPPEDIT 404 1 "10;" "6#\"#5" }{TEXT 326 
18 "             b)   " }{XPPEDIT 405 1 "12;" "6#\"#7" }{TEXT 327 17 "
             c)  " }{XPPEDIT 406 1 "14;" "6#\"#9" }{TEXT 328 18 "     \+
         d)  " }{XPPEDIT 407 1 "16;" "6#\"#;" }{TEXT 329 14 "         \+
 e)  " }{XPPEDIT 408 1 "18;" "6#\"#=" }{TEXT 330 12 "     \n f)   " }
{XPPEDIT 409 1 "20;" "6#\"#?" }{TEXT 331 19 "              g)   " }
{XPPEDIT 410 1 "22;" "6#\"#A" }{TEXT 332 17 "             h)  " }
{XPPEDIT 411 1 "24;" "6#\"#C" }{TEXT 333 18 "              i)  " }
{XPPEDIT 412 0 "26;" "6#\"#E" }{TEXT 403 15 "           j)  " }
{XPPEDIT 413 0 "28;" "6#\"#G" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 
3 "" 0 "" {TEXT 334 8 "Solution" }{TEXT 335 8 ": ( i )\n" }}{PARA 0 "
" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restar
t:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 43 "Integral := Int(15*x*
sqrt(x-2),x = 2 .. 3);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%)IntegralG
-%$IntG6$,$*(\"#:\"\"\"%\"xGF+,&F,F+\"\"#!\"\"#F+F.F+/F,;F.\"\"$" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "value(Integral); #Answer" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#\"#E" }}}{PARA 0 "" 0 "" {TEXT -1 0 "
" }}{PARA 0 "" 0 "" {TEXT -1 19 "Here are the steps:" }}{PARA 0 "" 0 "
" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 
0 "" {MPLTEXT 1 0 14 "with(student):" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 25 "substitution :=  u = x-2;" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>%-substitutionG/%\"uG,&%\"xG\"\"\"\"\"#!\"\"" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 59 "equivalentIntegral := change
var(substitution, Integral, u);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%3
equivalentIntegralG-%$IntG6$,$*(\"#:\"\"\",&\"\"#F+%\"uGF+F+F.#F+F-F+/
F.;\"\"!F+" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 52 "equivalentInt
egral :=  expand( equivalentIntegral );" }}{PARA 11 "" 1 "" {XPPMATH 
20 "6#>%3equivalentIntegralG,&*&\"#I\"\"\"-%$IntG6$*$%\"uG#F(\"\"#/F-;
\"\"!F(F(F(*&\"#:F(-F*6$*$)F-#\"\"$F/F(F0F(F(" }}}{EXCHG {PARA 0 "> " 
0 "" {MPLTEXT 1 0 26 "value(equivalentIntegral);" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#\"#E" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "
" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{SECT 0 {PARA 3 "" 
0 "" {TEXT -1 1 " " }{TEXT 342 17 "12. Calculate    " }{XPPEDIT 256 0 
"int((1+x^2)/(1+3*x+x^3),x = 1 .. 2);" "6#-%$intG6$*&,&\"\"\"F(*$%\"xG
\"\"#F(F(,(F(F(*&\"\"$F(F*F(F(*$F*F.F(!\"\"/F*;F(F+" }{TEXT 414 2 " .
" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 261 "" 0 "" {TEXT -1 4 "a)  \+
" }{XPPEDIT 18 0 "ln(2)/2;" "6#*&-%#lnG6#\"\"#\"\"\"F'!\"\"" }{TEXT 
-1 19 "               b)  " }{XPPEDIT 18 0 "ln(2);" "6#-%#lnG6#\"\"#" 
}{TEXT -1 23 "                   c)  " }{XPPEDIT 18 0 "2*ln(2);" "6#*&
\"\"#\"\"\"-%#lnG6#F$F%" }{TEXT -1 32 "                           d)  \+
 " }{XPPEDIT 18 0 "ln(3)/3;" "6#*&-%#lnG6#\"\"$\"\"\"F'!\"\"" }{TEXT 
-1 33 "                             e)  " }{XPPEDIT 18 0 "ln(3);" "6#-
%#lnG6#\"\"$" }{TEXT -1 20 "               \nf)  " }{XPPEDIT 18 0 "3*l
n(3);" "6#*&\"\"$\"\"\"-%#lnG6#F$F%" }{TEXT -1 17 "             g)  " 
}{XPPEDIT 18 0 "ln(3)-ln(2);" "6#,&-%#lnG6#\"\"$\"\"\"-F%6#\"\"#!\"\"
" }{TEXT -1 10 "      h)  " }{XPPEDIT 18 0 "2*ln(3)-2*ln(2);" "6#,&*&
\"\"#\"\"\"-%#lnG6#\"\"$F&F&*&F%F&-F(6#F%F&!\"\"" }{TEXT -1 16 "      \+
     i)   " }{XPPEDIT 18 0 "3*ln(3)-2*ln(2);" "6#,&*&\"\"$\"\"\"-%#lnG
6#F%F&F&*&\"\"#F&-F(6#F+F&!\"\"" }{TEXT -1 16 "            j)  " }
{XPPEDIT 18 0 "2*ln(3)-3*ln(2);" "6#,&*&\"\"#\"\"\"-%#lnG6#\"\"$F&F&*&
F*F&-F(6#F%F&!\"\"" }{TEXT -1 1 " " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}
{PARA 3 "" 0 "" {TEXT 343 8 "Solution" }{TEXT 344 8 ": ( d )\n" }}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "restart: with(student):" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 48 "Integral := Int((1+x^2)/(1+3
*x+x^3),x = 1 .. 2);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%)IntegralG-%
$IntG6$*&,&\"\"\"F**$)%\"xG\"\"#F*F*F*,(F*F**&\"\"$F*F-F*F**$)F-F1F*F*
!\"\"/F-;F*F." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "value(Inte
gral); #Answer" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,$*&#\"\"\"\"\"$F&-%
#lnG6#F'F&F&" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" 
{TEXT -1 19 "Here are the steps:" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}
{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
30 "substitution := u = 1+3*x+x^3;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#
>%-substitutionG/%\"uG,(\"\"\"F(*&\"\"$F(%\"xGF(F(*$)F+F*F(F(" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 59 "equivalentIntegral := change
var(substitution, Integral, u);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%3
equivalentIntegralG-%$IntG6$,$*&\"\"\"F**&\"\"$F*%\"uGF*!\"\"F*/F-;\"
\"&\"#:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "value( equivalen
tIntegral );" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,$*&#\"\"\"\"\"$F&-%#l
nG6#F'F&F&" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 
-1 0 "" }}}{SECT 0 {PARA 3 "" 0 "" {TEXT 295 33 "13. Calculate the are
a between   " }{XPPEDIT 456 0 "y = 3-x^2;" "6#/%\"yG,&\"\"$\"\"\"*$%\"
xG\"\"#!\"\"" }{TEXT 454 12 "    and     " }{XPPEDIT 457 0 "y = 2*x;" 
"6#/%\"yG*&\"\"#\"\"\"%\"xGF'" }{TEXT 455 2 ". " }}{PARA 0 "" 0 "" 
{TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 296 81 "a)  28/3              b)
  32/3          c)   12             d)  40/3          e) " }{TEXT 301 
1 " " }{TEXT 300 4 "44/3" }{TEXT 458 18 "                  " }}{PARA 
0 "" 0 "" {TEXT 297 89 "f)  16                  g)  52/3          h)  \+
56/3           i)  20              j)  64/3" }{TEXT -1 2 "  " }}{PARA 
3 "" 0 "" {TEXT -1 0 "" }}{PARA 3 "" 0 "" {TEXT 298 8 "Solution" }
{TEXT 299 8 ": ( b )\n" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "so
lve( 3 - x^2 = 2*x, x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$!\"$\"\"\"
" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 54 "plot([3 - x^2 , 2*x], x
 = -3 .. 1, color=[NAVY,BLUE]);" }}{PARA 13 "" 1 "" {GLPLOT2D 375 375 
375 {PLOTDATA 2 "6&-%'CURVESG6$7S7$$!\"$\"\"!$!\"'F*7$$!3cLLL$Q6G\"H!#
<$!3o[i([:qW[&F07$$!3bmm;M!\\p$GF0$!3]#=fC#)z#[]F07$$!37LLL))Qj^FF0$!3
k<WUb!*[rXF07$$!3ALLL=KvlEF0$!3pBX0@-C1TF07$$!3wmm;C2G!e#F0$!37eg]:'[y
l$F07$$!39LL$3yO5]#F0$!3yh63z\\=bKF07$$!3&*****\\nU)*=CF0$!3_6DT')[[^G
F07$$!3iLL$3WDTL#F0$!3u.aat:9[CF07$$!3))****\\d(Q&\\AF0$!3cVY\\@YUg?F0
7$$!3gmmmc4`i@F0$!3_[;aQ,aw;F07$$!3KLLLQW*e3#F0$!33K*pygb4N\"F07$$!33+
++q)>'**>F0$!3?s\"))\\C'z%)**!#=7$$!3.+++]5*H\">F0$!3wC5!QdZ`f'Fdo7$$!
3,+++I\"3&H=F0$!3)*o4Ox***4Z$Fdo7$$!3OLL$3k(p`<F0$!3g:*RkaTba(!#>7$$!3
smmmO;bj;F0$\"3sWlV@&ffK#Fdo7$$!3!ommm9'=(e\"F0$\"3#4=%He8S3[Fdo7$$!35
++]F\\N)\\\"F0$\"3=$pkB6D$\\vFdo7$$!3&ommmCC(>9F0$\"3/awEM1$Q%)*Fdo7$$
!3\"*****\\FRXL8F0$\"32D[BB1!>A\"F07$$!3)*****\\#=/8D\"F0$\"3q1!eG%yBM
9F07$$!3immmT&*el6F0$\"3'**Gd.-,9k\"F07$$!3omm;Wn(o3\"F0$\"3Gm'*)H%*)p
==F07$$!3PLLLeV(>+\"F0$\"3#\\]U_QZg*>F07$$!3hOLL3k%y8*Fdo$\"3Y&4x,j(*
\\;#F07$$!31-++DB:q$)Fdo$\"3wqHc+bS*H#F07$$!3XNLL$o@5a(Fdo$\"3[k\\r>*H
8V#F07$$!3S,+++'[Wo'Fdo$\"3+!eR\"p9=`DF07$$!3;/++]*ek%eFdo$\"3W['fu<*=
eEF07$$!39.++v3mN]Fdo$\"3CU*>b>@ku#F07$$!3b.++]ySNTFdo$\"3g$eT\">S)*GG
F07$$!3[pmmm/\\ELFdo$\"3gd<v6YM*)GF07$$!3y++++&)ziCFdo$\"3mxR[NiMRHF07
$$!3;NLL3_;!o\"Fdo$\"3)>1F([/xrHF07$$!3q1+++ISX#)Fdp$\"31fn$HL,K*HF07$
$!3)p3nm;%RY>!#?$\"3#yu\\:@'****HF07$$\"3lv****\\#G2A)Fdp$\"3ElRqi>C$*
HF07$$\"3jJLLL)G[k\"Fdo$\"3A`.4\"QXH(HF07$$\"3:)****\\7yh]#Fdo$\"3w9x0
72>PHF07$$\"3onmmm)fdL$Fdo$\"3if$>61F())GF07$$\"3almm;q7%=%Fdo$\"3-,S3
63$\\#GF07$$\"3pKLLe#pa-&Fdo$\"35maL(eYuu#F07$$\"3%*)******Rv&)z&Fdo$
\"3o[^IL_wjEF07$$\"3+LLL$GUYo'Fdo$\"3S@(QadbJb#F07$$\"3=lmmm5:xuFdo$\"
3]bCE>@#4W#F07$$\"3&4++]sI@K)Fdo$\"3O4,'>S@uI#F07$$\"3)3++]2%)38*Fdo$
\"3_8\"*3g&pi;#F07$$\"\"\"F*$\"\"#F*-%'COLOURG6&%$RGBG$\")!\\DP\"!\")F
_[l$\")viobFa[l-F$6$7SF'7$F.$!37nmmmFiDeF07$F4$!35LLLo!)*Qn&F07$F9$!3A
mmmwxE.bF07$F>$!3YmmmOk]J`F07$FC$!3_LLL[9cg^F07$FH$!3GmmmhN2-]F07$FM$!
3!******\\`oz$[F07$FR$!3Cnmm\")3DoYF07$FW$!3u*****\\^x!*\\%F07$Ffn$!3B
LLL8>1DVF07$F[o$!3kmmmw))yrTF07$F`o$!3;+++S(R#**RF07$Ffo$!30++++@)f#QF
07$F[p$!3-+++gi,fOF07$F`p$!3qmmm\"G&R2NF07$Ffp$!3XLLLtK5FLF07$F[q$!3eL
LL$HsV<$F07$F`q$!3?+++b)4n*HF07$Feq$!3rLLL$\\[%RGF07$Fjq$!3#)*****\\&y
!pm#F07$F_r$!3&******\\O3E]#F07$Fdr$!3CLLL$3z6L#F07$Fir$!3OLLL)[`P<#F0
7$F^s$!3ummm;([R+#F07$Fcs$!3Knmm\"Gpv#=F07$Fhs$!3S+++l/.u;F07$F]t$!34n
mmOV?3:F07$Fbt$!3G+++?(*)oL\"F07$Fgt$!3#3+++z\"Hp6F07$F\\u$!3j+++v@825
F07$Fau$!352+++d\"3F)Fdo7$Ffu$!3'*QLLL4)Hl'Fdo7$F[v$!3c,+++qfD\\Fdo7$F
`v$!3Kqmm;/LgLFdo7$Fev$!3M,+++13\\;Fdo7$Fjv$!3'R<MLL)y#*QF\\w7$F`w$\"3
8&*****\\c9W;Fdo7$Few$\"3Ejmmmwl*G$Fdo7$Fjw$\"3H'*****\\iN7]Fdo7$F_x$
\"3ONLLL(>:n'Fdo7$Fdx$\"31JLLLSDo$)Fdo7$Fix$\"3ammm^Q405F07$F^y$\"3y**
****z]rf6F07$Fcy$\"3gmmmc%GpL\"F07$Fhy$\"3/LLL8-V&\\\"F07$F]z$\"3=+++X
hUk;F07$Fbz$\"3=+++:o<E=F0Ffz-F\\[l6&F^[l$F*F*Ffdl$\"*++++\"Fa[l-%+AXE
SLABELSG6$Q\"x6\"Q!F]el-%%VIEWG6$;F(Fgz%(DEFAULTG" 1 2 0 1 10 0 2 9 1 
4 2 1.000000 45.000000 45.000000 0 0 "Curve 1" "Curve 2" }}}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 35 "int( (3 - x^2) - 2*x, x = -3 .. 1);
" }}{PARA 11 "" 1 "" {XPPMATH 20 "6##\"#K\"\"$" }}}{PARA 0 "" 0 "" 
{TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{SECT 0 {PARA 3 "" 0 
"" {TEXT 596 49 "14.  Calculate the area between the graphs of    " }
{XPPEDIT 597 0 "y = 6*x^2;" "6#/%\"yG*&\"\"'\"\"\"*$%\"xG\"\"#F'" }
{TEXT 598 9 "   and   " }{XPPEDIT 599 0 "y = x^3+8*x;" "6#/%\"yG,&*$%
\"xG\"\"$\"\"\"*&\"\")F)F'F)F)" }{TEXT 600 9 "    for  " }{XPPEDIT 
601 0 "x;" "6#%\"xG" }{TEXT 602 19 "  between 0 and  4." }}{PARA 0 "" 
0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 593 150 "a)  1            b
)  2             c)  3            d)  4           e)  5  \nf)   6     \+
      g)   7            h)  8             i)  9            j)  " }
{TEXT 594 2 "10" }{TEXT 595 1 "\n" }{TEXT -1 0 "" }}{PARA 0 "" 0 "" 
{TEXT 591 8 "Solution" }{TEXT 592 8 ":  ( h )" }{TEXT 603 1 "\n" }}
{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
29 "solve( 6*x^2 = x^3 + 8*x, x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%
\"\"!\"\"%\"\"#" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 68 "plot( [6
*x^2 , x^3 + 8*x], x=0..4, color=[blue, gold], thickness=2);" }}{PARA 
13 "" 1 "" {GLPLOT2D 623 589 589 {PLOTDATA 2 "6'-%'CURVESG6$7S7$$\"\"!
F)F(7$$\"3Hmmmm;')=()!#>$\"39m\"[d#H6hXF-7$$\"3RLLLe'40j\"!#=$\"3=q4bZ
q8&f\"F37$$\"3mmmm;6m$[#F3$\"38[^YDN9,PF37$$\"3fmmm;yYULF3$\"3pg9FjYD.
nF37$$\"3%HLL$eF>(>%F3$\"39Yj.Bc)p0\"!#<7$$\"3Qmmm\">K'*)\\F3$\"33yp[k
dy$\\\"FE7$$\"3P*****\\Kd,\"eF3$\"34p]Z)ova-#FE7$$\"3-mmm\"fX(emF3$\"3
m:CFrNLgEFE7$$\"3.*****\\U7Y](F3$\"3'='y'*eC:zLFE7$$\"3'QLLLV!pu$)F3$
\"3=\"*)\\7RE\"3UFE7$$\"3xmmm;c0T\"*F3$\"3#Gf>s'Q`8]FE7$$\"3#*******H,
Q+5FE$\"3b+H*pUiX+'FE7$$\"3)*******\\*3q3\"FE$\"3q:1GW2`*3(FE7$$\"3)**
*****p=\\q6FE$\"3.\"e;kI2.A)FE7$$\"3mmm;fBIY7FE$\"3\\$R'yAuh>$*FE7$$\"
3GLLLj$[kL\"FE$\"3/2QrOllr5!#;7$$\"3?LLL`Q\"GT\"FE$\"3w[B]!zDw>\"Fgp7$
$\"3!*****\\s]k,:FE$\"39=\"eUviHN\"Fgp7$$\"39LLL`dF!e\"FE$\"3+SR%R(GO)
\\\"Fgp7$$\"33++]sgam;FE$\"3]0\"fq[Dkm\"Fgp7$$\"3/++]<ep[<FE$\"3&e>&GP
AwM=Fgp7$$\"3QLLLe/TM=FE$\"3;EcyPq.>?Fgp7$$\"3JLL$eDBJ\">FE$\"3M+i?bV-
'>#Fgp7$$\"3immmTc-)*>FE$\"3-(\\a)yQE&R#Fgp7$$\"3Mmm;f`@'3#FE$\"3*>u$*
[rw8h#Fgp7$$\"3y****\\nZ)H;#FE$\"3(p@iE'=52GFgp7$$\"3YmmmJy*eC#FE$\"3Q
?5<UUVEIFgp7$$\"3')******R^bJBFE$\"3K^i^A'*ohKFgp7$$\"3f*****\\5a`T#FE
$\"3<4U_r7O+NFgp7$$\"3o****\\7RV'\\#FE$\"3NL!)on$4$RPFgp7$$\"3k*****\\
@fke#FE$\"3R[]^iF'Q,%Fgp7$$\"3/LLL`4NnEFE$\"3_W*[\\mc)oUFgp7$$\"3#****
***\\,s`FFE$\"3%Hh4()z%y\\XFgp7$$\"3[mm;zM)>$GFE$\"3^iPwb#y?\"[Fgp7$$
\"3$*******pfa<HFE$\"3:WzB#pWs5&Fgp7$$\"3#HLLeg`!)*HFE$\"3E\\,2a_*HR&F
gp7$$\"3w****\\#G2A3$FE$\"3N>wPR5++dFgp7$$\"3;LLL$)G[kJFE$\"35(yX8:r$3
gFgp7$$\"3#)****\\7yh]KFE$\"3')p`w(p4*RjFgp7$$\"3xmmm')fdLLFE$\"3O$QG`
JPwm'Fgp7$$\"3bmmm,FT=MFE$\"3)*)f\\$RsK6qFgp7$$\"3FLL$e#pa-NFE$\"3Q?()
f!)4qgtFgp7$$\"3!*******Rv&)zNFE$\"3y4p,/!G#*o(Fgp7$$\"3ILLLGUYoOFE$\"
3ymntwydu!)Fgp7$$\"3_mmm1^rZPFE$\"3)o_UC6@sU)Fgp7$$\"34++]sI@KQFE$\"3,
MR#)>U^6))Fgp7$$\"34++]2%)38RFE$\"3-Kl%4`ct=*Fgp7$$\"\"%F)$\"#'*F)-%'C
OLOURG6&%$RGBGF(F($\"*++++\"!\")-F$6$7SF'7$F+$\"3QS4W&G<<)pF37$F1$\"3.
i1FPDu38FE7$F7$\"36MB5P&\\A+#FE7$F<$\"3*e<)H3mJ6FFE7$FA$\"3bw6rYPpJMFE
7$FG$\"3iEc'*y(Hf6%FE7$FL$\"3/8nYLZEW[FE7$FQ$\"3m$)ym!)yBAcFE7$FV$\"3y
CB\\lPMEkFE7$Fen$\"3/n4&Q%\\6(G(FE7$Fjn$\"37.;FD5mw!)FE7$F_o$\"3%)y8bj
==/!*FE7$Fdo$\"3=l))QG)o/)**FE7$Fio$\"3=qV=xov'4\"Fgp7$F^p$\"3w!\\U.CE
1>\"Fgp7$Fcp$\"3CRWUh4'yI\"Fgp7$Fip$\"3&p;b1![D79Fgp7$F^q$\"3Q)G,-qF*R
:Fgp7$Fcq$\"3?w!)*eNe)e;Fgp7$Fhq$\"3_v`4L$*4'z\"Fgp7$F]r$\"3N%fu!HopL>
Fgp7$Fbr$\"37^gk4)=[3#Fgp7$Fgr$\"3)Qc`?[42B#Fgp7$F\\s$\"3U2#=9i`gR#Fgp
7$Fas$\"3%fejelapd#Fgp7$Ffs$\"3$\\()f*34MUFFgp7$F[t$\"3wS*G!\\>cHHFgp7
$F`t$\"3ZPPu7BrKJFgp7$Fet$\"3\"e$)f$y_QTLFgp7$Fjt$\"3%fbP\"\\-(Hb$Fgp7
$F_u$\"3++a(pU\\%*z$Fgp7$Fdu$\"3;`\"\\^CP;.%Fgp7$Fiu$\"3%eshI8:6H%Fgp7
$F^v$\"3:?+8qW(o`%Fgp7$Fcv$\"3O<rgPOZ<[Fgp7$Fhv$\"3I5XGH5>$4&Fgp7$F]w$
\"3!\\a/$yK'QR&Fgp7$Fbw$\"3.Bz&3D%[+dFgp7$Fgw$\"3PLH`:[ENgFgp7$F\\x$\"
3_]NO'Rt8P'Fgp7$Fax$\"3ED!*3V=LHnFgp7$Ffx$\"3kt!HfI/*)4(Fgp7$F[y$\"3#=
=$\\1&4;X(Fgp7$F`y$\"3eenhKZlryFgp7$Fey$\"3%y=?P1w>E)Fgp7$Fjy$\"3i_\")
G)y.Pp)Fgp7$F_z$\"3*)[g8#y$HA\"*FgpFcz-Fiz6&F[[l$\")+++!)F^[l$\")AR!)
\\F^[l$\")Vyg>F^[l-%*THICKNESSG6#\"\"#-%+AXESLABELSG6$Q\"x6\"Q!F_el-%%
VIEWG6$;F(Fdz%(DEFAULTG" 1 2 0 1 10 2 2 9 1 4 2 1.000000 45.000000 
45.000000 0 0 "Curve 1" "Curve 2" }}}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 78 "int((x^3 + 8*x) - 6*x^2, x = 0  .. 2) + int(6*x^2 - (
x^3 + 8*x), x = 2  .. 4);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\")" }}
}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{SECT 0 {PARA 3 "" 0 "" {TEXT 261 1 
" " }{TEXT 270 26 "15.  The Lorenz function  " }{XPPEDIT 462 0 "L;" "6
#%\"LG" }{TEXT 459 49 "  of a certain country has the following values
: " }}{PARA 3 "" 0 "" {TEXT -1 3 "   " }{XPPEDIT 460 0 "L(0) = 0,`  `*
L(20) = 5,`  `*L(40) = 10,`  `*L(60) = 28,`  `*L(80) = 50,`  `*L(90) =
 70,`  `*L(100) = 100;" "6)/-%\"LG6#\"\"!F'/*&%#~~G\"\"\"-F%6#\"#?F+\"
\"&/*&F*F+-F%6#\"#SF+\"#5/*&F*F+-F%6#\"#gF+\"#G/*&F*F+-F%6#\"#!)F+\"#]
/*&F*F+-F%6#\"#!*F+\"#q/*&F*F+-F%6#\"$+\"F+FL" }{TEXT 461 1 "." }}
{PARA 3 "" 0 "" {TEXT 464 22 "Using trapezoids and  " }{TEXT 466 3 "al
l" }{TEXT 467 78 "  the given (non-equally spaced) data, obtain an est
imate for the area under  " }{XPPEDIT 465 0 "y = L(x);" "6#/%\"yG-%\"L
G6#%\"xG" }{TEXT 463 1 "." }}{PARA 3 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "
" 0 "" {TEXT 468 87 "a)  2750            b)   2780           c)   2810
           d)  2840         e)  2870  " }{TEXT 471 1 " " }{TEXT 472 
18 "                  " }}{PARA 0 "" 0 "" {TEXT 469 40 "f)   2900     \+
       g)  2930           " }{TEXT -1 1 " " }{TEXT 470 48 "h)  2960   \+
         i)  2990          j)  3020  " }{TEXT -1 2 "  " }}{PARA 0 "" 
0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 3 "" 0 "" 
{TEXT 302 8 "Solution" }{TEXT 303 8 ": ( c )\n" }}{PARA 0 "" 0 "" 
{TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 86 "(0+5)/2*20 +
 (5+10)/2*20 + (10+28)/2*20 + (28+50)/2*20 + (50+70)/2*10 + (70+100)/2
*10;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"%5G" }}}{PARA 0 "" 0 "" 
{TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{SECT 0 {PARA 260 "" 
0 "" {TEXT -1 79 "16. By applying Simpson's Rule with four subinterval
s, what approximation of   " }{XPPEDIT 18 0 "Int(3*x^4,x = 0 .. 4);" "
6#-%$IntG6$*&\"\"$\"\"\"*$%\"xG\"\"%F(/F*;\"\"!F+" }{TEXT -1 15 "  is \+
obtained? " }}{PARA 0 "" 0 "" {TEXT 305 83 "a)  616           b)  620 \+
            c)   624          d)  628           e)  632  " }{TEXT 477 
2 "  " }{TEXT 308 13 "             " }}{PARA 0 "" 0 "" {TEXT 306 38 "f
)  636            g)  640            " }{TEXT -1 1 " " }{TEXT 307 44 "
h)  644           i)  648            j)  652" }}{PARA 0 "" 0 "" {TEXT 
-1 0 "" }}{PARA 3 "" 0 "" {TEXT 309 8 "Solution" }{TEXT 310 8 ": ( a )
\n" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 16 "f := x -> 3*x^4;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>
%\"fGf*6#%\"xG6\"6$%)operatorG%&arrowGF(,$*&\"\"$\"\"\")9$\"\"%F/F/F(F
(F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "Delta := (4-0)/4;" }
}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%&DeltaG\"\"\"" }}}{EXCHG {PARA 0 ">
 " 0 "" {MPLTEXT 1 0 47 "(f(0)+4*f(1) + 2*f(2) + 4*f(3) + f(4))*Delta/
3;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"$;'" }}}{EXCHG {PARA 0 "> " 0 
"" {MPLTEXT 1 0 48 "Answer:= student[simpson](3*x^4, x = 0 .. 4, 4);" 
}}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%'AnswerG,(\"$c#\"\"\"*&#\"\"%\"\"$
F'-%$SumG6$,$*&F+F'),&*&\"\"#F'%\"iGF'F'F'!\"\"F*F'F'/F5;F'F4F'F'*&#F4
F+F'-F-6$,$*&\"#[F')F5F*F'F'/F5;F'F'F'F'" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 16 "value( Answer );" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#
\"$;'" }}}{PARA 0 "" 0 "" {TEXT -1 1 " " }}{PARA 0 "" 0 "" {TEXT -1 0 
"" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{SECT 0 {PARA 3 "" 0 "" {TEXT 
271 11 "17.  If    " }{XPPEDIT 485 0 "y(x);" "6#-%\"yG6#%\"xG" }{TEXT 
484 58 "    is the unique solution of the initial value problem   " }
{XPPEDIT 480 0 "diff(y(x),x) = x*sqrt(y);" "6#/-%%diffG6$-%\"yG6#%\"xG
F**&F*\"\"\"-%%sqrtG6#F(F," }{TEXT 478 6 "  ,   " }{XPPEDIT 481 0 "y(2
) = 4;" "6#/-%\"yG6#\"\"#\"\"%" }{TEXT 479 21 "   \n then what is    \+
" }{XPPEDIT 483 0 "y(4);" "6#-%\"yG6#\"\"%" }{TEXT 482 3 " ? " }{TEXT 
272 2 " \n" }}{PARA 0 "" 0 "" {TEXT 604 159 "a)  21            b)  22 \+
            c)  23            d)  24           e)  25  \nf)   26      \+
     g)   27             h) 28             i)  39            j)  " }
{TEXT 605 2 "30" }{TEXT 606 1 "\n" }{TEXT -1 0 "" }}{PARA 0 "" 0 "" 
{TEXT -1 0 "" }}{PARA 3 "" 0 "" {TEXT -1 0 "" }{TEXT 304 0 "" }{TEXT 
-1 0 "" }}{PARA 3 "" 0 "" {TEXT 293 8 "Solution" }{TEXT 294 8 ": ( e )
\n" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 42 "eqn1 := int(1/sqrt(y), y) = int(x, x) + C;" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6#>%%eqn1G/,$*&\"\"#\"\"\"%\"yG#F)F(F),&*&F(!
\"\"%\"xGF(F)%\"CGF)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 46 "eqn
2 := C = solve( subs(\{y=4, x=2\}, eqn1), C);" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>%%eqn2G/%\"CG\"\"#" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 25 "eqn3 := subs(eqn2, eqn1);" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>%%eqn3G/,$*&\"\"#\"\"\"%\"yG#F)F(F),&*&F(!\"\"%\"xGF(F
)F(F)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "eqn4 := y = solve(
eqn3, y);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%eqn4G/%\"yG,(*&\"#;!\"
\"%\"xG\"\"%\"\"\"*&\"\"#F*F+F/F-F-F-" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 24 "eqn5 := subs(x=4, eqn4);" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>%%eqn5G/%\"yG\"#D" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}
}{SECT 0 {PARA 3 "" 0 "" {TEXT 275 17 "18.  Calculate   " }{XPPEDIT 
487 0 "int(1/x,x = -exp(1) .. -1);" "6#-%$intG6$*&\"\"\"F'%\"xG!\"\"/F
(;,$-%$expG6#F'F),$F'F)" }{TEXT 486 1 "." }}{PARA 3 "" 0 "" {TEXT 276 
1 "a" }{TEXT 274 3 ")  " }{XPPEDIT 493 0 "-ln(2);" "6#,$-%#lnG6#\"\"#!
\"\"" }{TEXT 488 16 "            b)  " }{XPPEDIT 494 0 "-ln(exp(1)-1);
" "6#,$-%#lnG6#,&-%$expG6#\"\"\"F+F+!\"\"F," }{TEXT 489 16 "          \+
  c)  " }{XPPEDIT 495 0 "-exp(1);" "6#,$-%$expG6#\"\"\"!\"\"" }{TEXT 
490 14 "          d)  " }{XPPEDIT 256 0 "-exp(1)+1;" "6#,&-%$expG6#\"
\"\"!\"\"F'F'" }{TEXT 501 18 "              e)  " }{XPPEDIT 496 0 "-1;
" "6#,$\"\"\"!\"\"" }{TEXT 491 15 "       \nf)     " }{XPPEDIT 497 0 "
ln(2);" "6#-%#lnG6#\"\"#" }{TEXT 492 18 "            g)    " }
{XPPEDIT 503 0 "ln(exp(1)-1);" "6#-%#lnG6#,&-%$expG6#\"\"\"F*F*!\"\"" 
}{TEXT 498 17 "            h)   " }{XPPEDIT 504 0 "exp(1);" "6#-%$expG
6#\"\"\"" }{TEXT 502 17 "            i)   " }{XPPEDIT 505 0 "1-exp(1);
" "6#,&\"\"\"F$-%$expG6#F$!\"\"" }{TEXT 499 21 "                j)   \+
" }{XPPEDIT 506 0 "1;" "6#\"\"\"" }{TEXT 500 8 "        " }{TEXT 290 
3 "\n  " }}{PARA 3 "" 0 "" {TEXT 291 8 "Solution" }{TEXT 292 8 ": ( e \+
)\n" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 67 "Answer := subs(x = -1, ln(abs(x))) - subs(x = -exp(1)
, ln(abs(x)));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%'AnswerG,&-%#lnG6#
-%$absG6#!\"\"\"\"\"-F'6#-F*6#,$-%$expG6#F-F,F," }}}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 17 "simplify(Answer);" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#!\"\"" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 
"" {TEXT -1 96 "Without absolute values is ok, but you must know some \+
more advanced facts about complex numbers:" }}{PARA 0 "" 0 "" {TEXT 
-1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 59 "upperEndpointEvaluation := simplify( subs(x = -1, ln(
x)) );" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%8upperEndpointEvaluationG*
&%#PiG\"\"\"^#F'F'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 64 "lower
EndpointEvaluation := simplify( subs(x = -exp(1), ln(x)) );" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6#>%8lowerEndpointEvaluationG,&\"\"\"F&*&%#PiG
F&^#F&F&F&" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 50 "upperEndpoint
Evaluation - lowerEndpointEvaluation;" }}{PARA 11 "" 1 "" {XPPMATH 20 
"6#!\"\"" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 
0 "" }}}{SECT 0 {PARA 260 "" 0 "" {TEXT 277 16 "19. Calculate   " }
{XPPEDIT 18 0 "int(tan(x),x = 0 .. Pi/3);" "6#-%$intG6$-%$tanG6#%\"xG/
F);\"\"!*&%#PiG\"\"\"\"\"$!\"\"" }{TEXT 507 9 ".\n\n\na)   " }
{XPPEDIT 18 0 "1/2;" "6#*&\"\"\"F$\"\"#!\"\"" }{TEXT 517 1 " " }
{XPPEDIT 18 0 "ln(2);" "6#-%#lnG6#\"\"#" }{TEXT 516 16 "           b) \+
  " }{XPPEDIT 265 0 "ln(2);" "6#-%#lnG6#\"\"#" }{TEXT 508 17 "        \+
     c)  " }{XPPEDIT 266 0 "2*ln(2);" "6#*&\"\"#\"\"\"-%#lnG6#F$F%" }
{TEXT 509 15 "          d)   " }{XPPEDIT 18 0 "1/2;" "6#*&\"\"\"F$\"\"
#!\"\"" }{TEXT 518 1 " " }{XPPEDIT 256 0 "ln(3);" "6#-%#lnG6#\"\"$" }
{TEXT 514 14 "          e)  " }{XPPEDIT 267 0 "ln(3);" "6#-%#lnG6#\"\"
$" }{TEXT 510 14 "       \nf)    " }{XPPEDIT 268 0 "2*ln(3);" "6#*&\"
\"#\"\"\"-%#lnG6#\"\"$F%" }{TEXT 511 17 "            g)   " }{XPPEDIT 
272 0 "3*ln(3);" "6#*&\"\"$\"\"\"-%#lnG6#F$F%" }{TEXT 512 13 "        \+
  h) " }{XPPEDIT 273 0 "1;" "6#\"\"\"" }{TEXT 515 26 "                \+
     i)   " }{XPPEDIT 274 0 "2;" "6#\"\"#" }{TEXT 513 25 "            \+
         j)  " }{XPPEDIT 275 0 "sqrt(2);" "6#-%%sqrtG6#\"\"#" }}{PARA 
3 "" 0 "" {TEXT 288 1 "\n" }{TEXT 615 8 "Solution" }{TEXT 289 8 ": ( b
 )\n" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 20 "J := int(tan(x), x);" }}{PARA 11 "" 1 "" {XPPMATH 20 
"6#>%\"JG,$-%#lnG6#-%$cosG6#%\"xG!\"\"" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 46 "simplify( subs(x = Pi/3, J) - subs(x = 0, J));" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#-%#lnG6#\"\"#" }}}{PARA 0 "" 0 "" 
{TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{SECT 0 {PARA 3 "" 0 
"" {TEXT 280 16 "20. Calculate   " }{XPPEDIT 520 0 "int(sec(x),x = 0 .
. Pi/4);" "6#-%$intG6$-%$secG6#%\"xG/F);\"\"!*&%#PiG\"\"\"\"\"%!\"\"" 
}{TEXT 519 2 ".\n" }}{PARA 260 "" 0 "" {TEXT 279 5 "a)   " }{XPPEDIT 
526 1 "ln(2)/2;" "6#*&-%#lnG6#\"\"#\"\"\"F'!\"\"" }{TEXT 521 18 "     \+
       b)    " }{XPPEDIT 527 1 "ln(3)/2;" "6#*&-%#lnG6#\"\"$\"\"\"\"\"
#!\"\"" }{TEXT 281 18 "              c)  " }{XPPEDIT 528 1 "ln(1+sqrt(
2));" "6#-%#lnG6#,&\"\"\"F'-%%sqrtG6#\"\"#F'" }{TEXT 282 13 "         \+
d)  " }{XPPEDIT 529 1 "ln(1+sqrt(3));" "6#-%#lnG6#,&\"\"\"F'-%%sqrtG6#
\"\"$F'" }{TEXT 283 13 "         e)  " }{XPPEDIT 530 0 "ln(2+sqrt(3));
" "6#-%#lnG6#,&\"\"#\"\"\"-%%sqrtG6#\"\"$F(" }{TEXT 522 10 "   \nf)   \+
 " }{XPPEDIT 531 1 "ln(2);" "6#-%#lnG6#\"\"#" }{TEXT 523 18 "         \+
    g)   " }{XPPEDIT 532 1 "ln(3+sqrt(2));" "6#-%#lnG6#,&\"\"$\"\"\"-%
%sqrtG6#\"\"#F(" }{TEXT 284 10 "      h)  " }{XPPEDIT 533 0 "ln(2*sqrt
(2));" "6#-%#lnG6#*&\"\"#\"\"\"-%%sqrtG6#F'F(" }{TEXT 285 16 "        \+
     i) " }{XPPEDIT 534 0 "ln(2*sqrt(3));" "6#-%#lnG6#*&\"\"#\"\"\"-%%
sqrtG6#\"\"$F(" }{TEXT 524 18 "              j)  " }{XPPEDIT 535 1 "ln
(sqrt(2)+sqrt(3));" "6#-%#lnG6#,&-%%sqrtG6#\"\"#\"\"\"-F(6#\"\"$F+" }
{TEXT 525 2 "  " }{TEXT 278 1 "\n" }}{PARA 3 "" 0 "" {TEXT 286 8 "Solu
tion" }{TEXT 287 8 ": ( c )\n" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "J := int(sec(x),x);" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"JG-%#lnG6#,&-%$secG6#%\"xG\"\"\"-%
$tanGF+F-" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 46 "simplify( subs
(x = Pi/4, J) - subs(x = 0, J));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%
#lnG6#,&\"\"\"F'*$\"\"##F'F)F'" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}
{SECT 0 {PARA 3 "" 0 "" {TEXT -1 4 "Code" }}{PARA 0 "" 0 "" {TEXT 542 
23 "For graph of Problem 1:" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 79 "fnPlot := plot( [[0,1],[1,4],[2,2],
[4,3],[5,0],[6,2]],thickness=3,color=BLACK):" }}}{EXCHG {PARA 0 "> " 
0 "" {MPLTEXT 1 0 91 "for j from 1 to 4 do\nhorizPlot[j] := plot(j, x \+
= 0..6, color = COLOR(RGB,0.8,0.8,0.8)):\nod:" }}}{EXCHG {PARA 0 "> " 
0 "" {MPLTEXT 1 0 95 "for j from 1 to 6 do\nvertPlot[j] := plot([j, y,
 y = 0..4], color = COLOR(RGB,0.8,0.8,0.8)):\nod:" }}}{EXCHG {PARA 0 "
> " 0 "" {MPLTEXT 1 0 78 "plots[display](fnPlot,seq(horizPlot[j], j = \+
1..4),seq(vertPlot[j], j = 1..6)):" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 0 "" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" 
{TEXT -1 11 "Shaded plot" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 79 "fnPlot := plot( [[0,1],[1,4],[2,2],
[4,3],[5,0],[6,2]],thickness=3,color=BLACK):" }}}{EXCHG {PARA 0 "> " 
0 "" {MPLTEXT 1 0 91 "for j from 1 to 4 do\nhorizPlot[j] := plot(j, x \+
= 0..6, color = COLOR(RGB,0.8,0.8,0.8)):\nod:" }}}{EXCHG {PARA 0 "> " 
0 "" {MPLTEXT 1 0 95 "for j from 1 to 6 do\nvertPlot[j] := plot([j, y,
 y = 0..4], color = COLOR(RGB,0.8,0.8,0.8)):\nod:" }}}{EXCHG {PARA 0 "
> " 0 "" {MPLTEXT 1 0 82 "rect1 := plottools[rectangle]( [0,4] , [2,0]
, color = COLOR(RGB,0.99,0.99,0.90) ):" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 82 "rect2 := plottools[rectangle]( [2,3] , [4,0], color =
 COLOR(RGB,0.99,0.99,0.90) ):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 82 "rect3 := plottools[rectangle]( [4,3] , [6,0], color = COLOR(RGB,
0.99,0.99,0.90) ):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 96 "plots
[display](fnPlot,seq(horizPlot[j], j = 1..4),seq(vertPlot[j], j = 1..6
),rect1,rect2,rect3);" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 
0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}}{MARK "13 13 1 \+
0" 0 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }