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{SECT 0 {EXCHG {PARA 18 "" 0 "" {TEXT 258 20 "Math 132 Summer 1998" }}
{PARA 18 "" 0 "" {TEXT 257 8 "Exam 1\n\n" }}}{SECT 0 {PARA 3 "" 0 "" 
{TEXT 256 13 "Instructions:" }{TEXT 259 4 "    " }{TEXT 260 40 "Only t
he right side pages will be graded" }{TEXT 261 10 ".  Do all " }{TEXT 
263 7 "scratch" }{TEXT 264 186 " work on the left side and then neatly
 present your solution on the right. Your solution must include not on
ly the answer but also all the work that is necessary to obtain the an
swer. \n\n" }}}{SECT 0 {PARA 3 "" 0 "" {TEXT -1 54 "1. Find the area o
f the region bounded by the curves  " }{XPPEDIT 19 1 "y=x" "/%\"yG%\"x
G" }{TEXT -1 6 "  and " }{XPPEDIT 19 1 "y=x^2" "/%\"yG*$%\"xG\"\"#" }
{TEXT -1 2 ". " }}{PARA 3 "" 0 "" {TEXT -1 0 "" }}{PARA 3 "" 0 "" 
{TEXT 265 7 "Answer:" }{TEXT 266 1 " " }{TEXT -1 2 "  " }}{PARA 0 "" 
0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 ">
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0 0 0 0 0 0 }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 35 "Area := int( \+
x - x^2 , x = 0 .. 1);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%AreaG#\"
\"\"\"\"'" }}}}{SECT 0 {PARA 3 "" 0 "" {TEXT -1 42 "2. Find the area o
f the region bounded by " }{XPPEDIT 19 1 "y=x/2" "/%\"yG*&%\"xG\"\"\"
\"\"#!\"\"" }{TEXT -1 6 " and  " }{XPPEDIT 19 1 "y^2=8-x" "/*$%\"yG\"
\"#,&\"\")\"\"\"%\"xG!\"\"" }{TEXT -1 2 ".\n" }}{PARA 3 "" 0 "" {TEXT 
267 7 "Answer:" }{TEXT 268 1 " " }{TEXT -1 2 "  " }}{PARA 0 "" 0 "" 
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"" {MPLTEXT 1 0 30 "solve( (x/2)^2 = 8 - x , x ); " }}{PARA 11 "" 1 "
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12 "with(plots):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 61 "implici
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{MPLTEXT 1 0 43 "Area := int( (8-y^2) - 2*y , y = -4 .. 2 );" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6#>%%AreaG\"#O" }}}{PARA 0 "" 0 "" {TEXT -1 0 
"" }}}{SECT 0 {PARA 3 "" 0 "" {TEXT -1 34 "3.  What is the average val
ue of  " }{XPPEDIT 19 1 "y=1/(1+x^2)" "/%\"yG*&\"\"\"F%,&F%F%*$%\"xG\"
\"#F%!\"\"" }{TEXT -1 7 "  for  " }{XPPEDIT 19 1 "x" "I\"xG6\"" }
{TEXT -1 17 " in the interval " }{XPPEDIT 19 1 "[1/sqrt(3),sqrt(3)" "7
$*&\"\"\"F$-%%sqrtG6#\"\"$!\"\"-F&6#F(" }{TEXT -1 4 "?  \n" }}{PARA 0 
"" 0 "" {TEXT -1 0 "" }}{PARA 3 "" 0 "" {TEXT 269 7 "Answer:" }{TEXT 
270 1 " " }{TEXT -1 2 "  " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "
" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 109 "Aver
age := 1/(sqrt(3) - 1/sqrt(3))*Int(1/(1+x^2) , \n                     \+
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6#>%(AverageG,$*&\"\"$#\"\"\"\"\"#-%$IntG6$*$,&F)F)*$%\"xGF*F)!\"\"/F1
;,$*$F'F(#F)F'F6F)F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "val
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0 "" {TEXT -1 17 "4. The graph of  " }{XPPEDIT 19 1 "y=sqrt(sin(x)) " 
"/%\"yG-%%sqrtG6#-%$sinG6#%\"xG" }{TEXT -1 6 "  for " }{XPPEDIT 19 1 "
x" "I\"xG6\"" }{TEXT -1 17 " in the interval " }{XPPEDIT 19 1 "[0,Pi" 
"7$\"\"!%#PiG" }{TEXT -1 77 " is rotated about the x-axis. What is the
 volume of the solid of revolution?\n" }}{PARA 3 "" 0 "" {TEXT -1 1 "
\n" }{TEXT 271 7 "Answer:" }{TEXT 272 1 " " }}{PARA 0 "" 0 "" {TEXT 
-1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 59 "implicitplot( y = \+
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{PARA 0 "> " 0 "" {MPLTEXT 1 0 49 "Volume := Int( Pi*sqrt(sin(x))^2 , \+
x = 0 .. Pi );" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%'VolumeG-%$IntG6$*
&%#PiG\"\"\"-%$sinG6#%\"xGF*/F.;\"\"!F)" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 14 "value(Volume);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,$%
#PiG\"\"#" }}}}{SECT 0 {PARA 3 "" 0 "" {TEXT -1 52 "5. The region in t
he first quadrant that lies under " }{XPPEDIT 19 1 "y=4sqrt(x) " "/%\"
yG*&\"\"%\"\"\"-%%sqrtG6#%\"xGF&" }{TEXT -1 11 " and above " }
{XPPEDIT 19 1 "y=(x/2)^3" "/%\"yG*$*&%\"xG\"\"\"\"\"#!\"\"\"\"$" }
{TEXT -1 77 " is rotated about the y-axis. What is the volume of the s
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:" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 298 19 "Dis
k-Washer Method:" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" 
{TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 56 "Volume := In
t( Pi*2^2 - Pi*(2-y^(1/3))^2 , y = 0 .. 8 );" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>%'VolumeG-%$IntG6$,&%#PiG\"\"%*&F)\"\"\",&\"\"#F,*$%\"
yG#F,\"\"$!\"\"F.F3/F0;\"\"!\"\")" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 24 "simplify(value(Volume));" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#,$%#PiG#\"$W\"\"\"&" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }
}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 297 25 "Cylindr
ical Shell Method:" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" 
{TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 48 "Volume := In
t( 2*Pi*(8-x^3)*(2-x) , x = 0 .. 2);" }}{PARA 11 "" 1 "" {XPPMATH 20 "
6#>%'VolumeG-%$IntG6$,$*(%#PiG\"\"\",&\"\")F+*$%\"xG\"\"$!\"\"F+,&\"\"
#F+F/F1F+F3/F/;\"\"!F3" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "v
alue(Volume);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,$%#PiG#\"$W\"\"\"&" 
}}}{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 25 "
8. A spring is stretched " }{XPPEDIT 19 1 "xi" "I#xiG6\"" }{TEXT -1 
53 " meters beyond its equilibrium position.  The number " }{XPPEDIT 
19 1 "xi" "I#xiG6\"" }{TEXT -1 37 " is not noted but it is noted that \+
a " }{XPPEDIT 19 1 "3N" "*&\"\"$\"\"\"%\"NGF$" }{TEXT -1 81 "  force i
s needed to maintain the spring at that position. It is also noted tha
t " }{XPPEDIT 19 1 "5J" "*&\"\"&\"\"\"%\"JGF$" }{TEXT -1 47 " of work \+
must be done to stretch the spring an " }{TEXT 262 10 "additional" }
{TEXT -1 1 " " }{XPPEDIT 19 1 "1m" "*&\"\"\"F#%\"mGF#" }{TEXT -1 119 "
  (that is, from the unrecorded stretched position). Find the value of
 the spring constant and determine the value of  " }{XPPEDIT 19 1 "xi
" "I#xiG6\"" }{TEXT -1 2 ".\n" }}{PARA 3 "" 0 "" {TEXT 291 7 "Answer:
" }{TEXT 292 1 " " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" 
{TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "equation1 :=
 3 = k*xi;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%*equation1G/\"\"$*&%\"
kG\"\"\"%#xiGF)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 43 "equation
2 := 5 = int(k*x , x = xi .. xi+1);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6
#>%*equation2G/\"\"&,&*&%\"kG\"\"\"%#xiGF*F*F)#F*\"\"#" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 48 "solve( \{ equation1 , equation2 \} \+
, \{ k , xi \} );" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#<$/%#xiG#\"\"$\"
\"%/%\"kGF(" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{SECT 0 {PARA 3 "" 0 
"" {TEXT -1 5 "9. A " }{XPPEDIT 19 1 "30ft" "*&\"#I\"\"\"%#ftGF$" }
{TEXT -1 81 "  cable is suspended from the top of a building. The cabl
e is uniform and weighs " }{XPPEDIT 19 1 "1lb" "*&\"\"\"F#%#lbGF#" }
{TEXT -1 113 " per foot. A bucket of cement is attached to the end of \+
the cable. The cable is cranked so that the bucket rises " }{XPPEDIT 
19 1 "20ft" "*&\"#?\"\"\"%#ftGF$" }{TEXT -1 23 ". If doing so requires
 " }{XPPEDIT 19 1 "2000ft-lbs" ",&*&\"%+?\"\"\"%#ftGF%F%%$lbsG!\"\"" }
{TEXT -1 53 " work, then how much does the bucket of cement weigh?" }}
{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 3 "" 0 "" {TEXT 293 7 "Answer:" 
}{TEXT 294 1 " " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" 
{TEXT -1 6 "Let   " }{XPPEDIT 295 1 "W" "I\"WG6\"" }{TEXT 296 1 " " }
{TEXT -1 90 "  be the unknown weight of the bucket of cement. We then \+
have the following work equation:" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 62 "work_equation := 2000 = W*20
 + 10*20 + int( x , x = 0 .. 20); " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#
>%.work_equationG/\"%+?,&%\"WG\"#?\"$+%\"\"\"" }}}{EXCHG {PARA 0 "> " 
0 "" {MPLTEXT 1 0 27 "solve( work_equation , W );" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#\"#!)" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 
"" {TEXT -1 0 "" }}}{SECT 0 {PARA 3 "" 0 "" {TEXT -1 14 "10.  Evaluate
 " }{XPPEDIT 19 1 "int(x*sin(x),x=0..Pi" "-%$intG6$*&%\"xG\"\"\"-%$sin
G6#F&F'/F&;\"\"!%#PiG" }{TEXT -1 87 ". (You must show your work. A cal
culator-generated numerical answer is not acceptable.)" }}{PARA 0 "" 
0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 3 "" 0 "" 
{TEXT 289 7 "Answer:" }{TEXT 290 1 " " }}{PARA 3 "" 0 "" {TEXT -1 1 " \+
" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "with(student):" }}{PARA 
7 "" 1 "" {TEXT -1 29 "Warning, new definition for D" }}}{EXCHG {PARA 
0 "> " 0 "" {MPLTEXT 1 0 51 "J := intparts( Int( x*sin(x) , x = 0 .. P
i ) , x );" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"JG,&%#PiG\"\"\"-%$In
tG6$,$-%$cosG6#%\"xG!\"\"/F/;\"\"!F&F0" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 9 "value(J);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%#PiG" }}
}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}
{SECT 0 {PARA 3 "" 0 "" {TEXT -1 13 "11. Evaluate " }{XPPEDIT 19 1 "in
t(ln(x^(3)),x=1..exp(1)" "-%$intG6$-%#lnG6#*$%\"xG\"\"$/F);\"\"\"-%$ex
pG6#F-" }{TEXT -1 90 ". (You must show your work. A calculator-generat
ed numerical answer is not acceptable.)   " }}{PARA 0 "" 0 "" {TEXT 
-1 0 "" }}{PARA 3 "" 0 "" {TEXT 287 7 "Answer:" }{TEXT 288 1 " " }}
{PARA 3 "" 0 "" {TEXT -1 1 " " }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 14 "with(student):" }}{PARA 7 "" 1 "" {TEXT -1 29 "Warning, new defi
nition for D" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 39 "J :=  Int( \+
ln(x^3) , x = 1 .. exp(1)) ;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"JG
-%$IntG6$-%#lnG6#*$%\"xG\"\"$/F,;\"\"\"-%$expG6#F0" }}}{EXCHG {PARA 0 
"> " 0 "" {MPLTEXT 1 0 10 "expand(J);" }}{PARA 11 "" 1 "" {XPPMATH 20 
"6#,$-%$IntG6$-%#lnG6#%\"xG/F*;\"\"\"-%$expG6#F-\"\"$" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 55 "J := in
tparts( 3*Int(ln(x),x = 1 .. exp(1))  , ln(x) );" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>%\"JG,&-%$expG6#\"\"\"\"\"$-%$IntG6$F)/%\"xG;F)F&!\"$
" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "value(J);" }}{PARA 11 "
" 1 "" {XPPMATH 20 "6#\"\"$" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 
0 "" 0 "" {TEXT -1 0 "" }}}{SECT 0 {PARA 3 "" 0 "" {TEXT -1 18 "12.  S
uppose that " }{XPPEDIT 19 1 "n" "I\"nG6\"" }{TEXT -1 31 "  is a const
ant different from " }{XPPEDIT 19 1 "-1" ",$\"\"\"!\"\"" }{TEXT -1 11 
". Evaluate " }{XPPEDIT 19 1 "int(x^n*ln(x),x" "-%$intG6$*&)%\"xG%\"nG
\"\"\"-%#lnG6#F'F)F'" }{TEXT -1 1 "." }}{PARA 3 "" 0 "" {TEXT 285 7 "A
nswer:" }{TEXT 286 1 " " }}{PARA 3 "" 0 "" {TEXT -1 1 " " }}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "with(student):" }}{PARA 7 "" 1 "" 
{TEXT -1 29 "Warning, new definition for D" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 45 "J := intparts( Int( x^n*ln(x) , x) , ln(x) );" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"JG,&*(-%#lnG6#%\"xG\"\"\")F*,&%\"n
GF+F+F+F+F-!\"\"F+-%$IntG6$*(F*F/F,F+F-F/F*F/" }}}{EXCHG {PARA 0 "> " 
0 "" {MPLTEXT 1 0 9 "value(J);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,&*(
-%#lnG6#%\"xG\"\"\")F(,&%\"nGF)F)F)F)F+!\"\"F)*&F*F)F+!\"#F-" }}}}}
{MARK "9 0 0" 11 }{VIEWOPTS 1 1 0 1 1 1803 }