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152 "The  words and symbols that are used in this worksheet have been \+
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ctEquality := plot(x,x=0..100,scaling = constrained, color=WHEAT):" }}
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]:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 104 "Ly := [0,3.6,3.6+9.0
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274 11 "interpolate" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "
" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" 
{TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 921 "interpolate
 := proc()\nlocal i__,LIST,X__:\nif nargs <> 3\n   then \n   ERROR(`in
terpolate expects 3 arguments.`);\nelif not type(args[1],\{name,proced
ure\})\n   then\n   ERROR(`interpolate expects its first argument to b
e a name or a procedure.`);\nelif not type(args[2],list) then\n   ERRO
R(`interpolate expects its second argument to be a list of real number
s.`);\nelif not type(args[3],algebraic) then\n   ERROR(`interpolate ex
pects its third argument to be an algebraic expression.`);\nelif not t
ype(nops(args[2]),posint) then\nERROR(`The number of entries in the se
cond argument of interpolate must be a positive integer.`);\nelse\n  L
IST := []:\n  for i__ from 1 to nops(args[2]) do\n  if not type(op(i__
,args[2]),realcons) then\n  ERROR(`The entries of interpolate's second
 argument must be real constants.`);\nfi:\nLIST := [op(LIST),args[1](a
rgs[2][i__])]:\nod:\nRETURN(subs(X__=args[3],collect(interp(args[2],LI
ST,X__),X__)));\nfi:\nend:" }}}}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 17 " \+
Description of  " }{TEXT 275 11 "interpolate" }}{SECT 0 {PARA 0 "" 0 "
" {TEXT 26 10 "Function: " }{TEXT 261 12 " interpolate" }{TEXT -1 48 "
 - returns the Lagrange interpolating polynomial" }}{PARA 0 "" 0 "usag
e" {TEXT 26 17 "Calling Sequence:" }{TEXT -1 1 "\n" }{TEXT 269 4 "   i
" }{TEXT 272 10 "nterpolate" }{TEXT 273 9 "(f, L, x)" }}{PARA 0 "" 0 "
" {TEXT 26 11 "Parameters:" }{TEXT -1 3 "\n  " }{TEXT 262 1 " " }
{TEXT 264 1 "f" }{TEXT 263 3 " - " }{TEXT -1 48 "a function name or pr
ocedure, or an equation\n   " }{TEXT 266 1 "L" }{TEXT 265 3 " - " }
{TEXT -1 26 "a list of real numbers\n   " }{TEXT 268 1 "x" }{TEXT 267 
3 " - " }{TEXT -1 23 "an algebraic expression" }}}{SECT 0 {PARA 0 "" 
0 "synopsis" {TEXT 26 12 "Description:" }}{PARA 15 "" 0 "" {TEXT -1 
10 "The call  " }{TEXT 270 1 "i" }{TEXT 276 10 "nterpolate" }{TEXT 
277 22 "(f, [x0,x1,...,xN], x)" }{TEXT -1 58 ", returns the Lagrange i
nterpolating polynomial of degree " }{TEXT 278 2 " N" }{TEXT -1 34 "  \+
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