{VERSION 6 0 "IBM INTEL NT" "6.0" }
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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 "Warni
ng" -1 7 1 {CSTYLE "" -1 -1 "Courier" 1 10 0 0 255 1 2 2 2 2 2 1 1 1 
3 1 }1 1 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Error" -1 8 1 {CSTYLE "" 
-1 -1 "Courier" 1 10 255 0 255 1 2 2 2 2 2 1 1 1 3 1 }1 1 0 0 0 0 1 0 
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{PSTYLE "Maple Output" -1 12 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 
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" -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 2 0 2 0 
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0 0 1 2 2 2 2 2 2 1 1 1 1 }1 1 0 0 0 0 2 0 2 0 2 2 0 1 }}
{SECT 0 {EXCHG {PARA 202 "> " 0 "" {MPLTEXT 1 -1 8 "restart;" }}}
{EXCHG {PARA 202 "> " 0 "" {MPLTEXT 1 -1 21 "f:=x->(x/sin(x))^2;\n\n" 
}}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"fGj+6#%\"xG6\"6$%)operatorG%&arr
owGF(*&9$\"\"#-%$sinG6#F-!\"#F(F(F(6#\"\"!" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 20 "SumFirstn_1:=proc(n)" }}{PARA 0 "> " 0 "" {MPLTEXT 
1 0 77 "I:=0;\nfor i from 1 to n do\nI:=I+i;\nend do;\nprint(seq(i,i=1
..n));\nI;\nend proc:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}{PARA 
0 "> " 0 "" {MPLTEXT 1 0 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}
{PARA 7 "" 1 "" {TEXT -1 69 "Warning, `I` is implicitly declared local
 to procedure `SumFirstn_1`\n" }}{PARA 7 "" 1 "" {TEXT -1 69 "Warning,
 `i` is implicitly declared local to procedure `SumFirstn_1`\n" }}
{PARA 7 "" 1 "" {TEXT -1 78 "Warning, imaginary unit `I` used as a loc
al variable in procedure SumFirstn_1\n" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 15 "SumFirstn_1(5);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6'\"
\"\"\"\"#\"\"$\"\"%\"\"&" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"#:" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "SumFirstn_2:=proc(n)" }}
{PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "add(i,i=1..n);" }}{PARA 0 "> " 0 "
" {MPLTEXT 1 0 9 "end proc;" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#>%,SumFirstn_2Gj+6#%\"nG6\"F(F(-%$addG
6$%\"iG/F,;\"\"\"9$F(F(F(6#\"\"!" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 15 "SumFirstn_2(5);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"
#:" }}}{EXCHG {PARA 11 "" 1 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 
"" {MPLTEXT 1 0 237 "SecantLines:=proc(f,a0,a1,n)\n\nglobal SecL, A, M
,L;\nA:=[seq(a1-j*(a1-a0)/n,j=0..n-1)];\n\nfor i from 1 to n-1 do\n\nM
[i]:=(f(A[i])-f(a0))/(A[i]-a0);\n\nSecL[i]:=M[i]*(x-a0)+(f(a0));\nend \+
do;\nplot([f4(x),seq(SecL[i](x),i=1..n-1)],x=0..3,y=0..20);" }}{PARA 
0 "> " 0 "" {MPLTEXT 1 0 9 "end proc;" }}{PARA 7 "" 1 "" {TEXT -1 69 "
Warning, `i` is implicitly declared local to procedure `SecantLines`\n
" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%,SecantLinesGj+6&%\"fG%#a0G%#a1G
%\"nG6#%\"iG6\"F-C%>%\"AG7#-%$seqG6$,&9&\"\"\"*(%\"jGF7,&F6F79%!\"\"F7
9'F<F</F9;\"\"!,&F=F7F7F<?(8$F7F7FA%%trueGC$>&%\"MG6#FC*&,&-9$6#&F0FIF
7-FM6#F;F<F7,&FOF7F;F<F<>&%%SecLGFI,&*&FGF7,&%\"xGF7F;F<F7F7FPF7-%%plo
tG6%7$-%#f4G6#FY-F36$-FTFjn/FC;F7FA/FY;F@\"\"$/%\"yG;F@\"#?F-6&FUF0FH%
\"LGF-6&F@F@F@\"'I)*e" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "Se
cantLines(f4,1,5,3);" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}{PARA 8 
"" 1 "" {TEXT -1 35 "Error, (in plot) invalid arguments\n" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "eval(SecL);" }}{PARA 0 "> " 0 "" 
{MPLTEXT 1 0 5 "L[1];" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6#K%&TABLEG6#7$/\"\"\"*&F(F(*$)-%$sinG6#F(\"\"
#F(!\"\"/F/F)Q(pprint06\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#&%\"LG6#
\"\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "seq(f4(A[i])-f4(1
),i=1..4);" }}{PARA 8 "" 1 "" {TEXT -1 34 "Error, invalid subscript se
lector\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "plot(SecL[1](x)
,x=0..3);" }}{PARA 8 "" 1 "" {TEXT -1 35 "Error, (in plot) invalid arg
uments\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "M[2];" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6#,&*&#\"$@\"\"#C\"\"\"*&F(F(*$)-%$sinG6##\"#6
\"\"$\"\"#F(!\"\"F(F(*&#F1\"\")F(*&F(F(*$)-F-6#F(F2F(F3F(F3" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 30 "m1:=(f4(1.4)-f4(.5))/(1.4-.5);" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>%#m1G$\"+)4RS.\"!\"*" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 15 "a1:=.5;a2:=1.0;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%
#a1G$\"\"&!\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#a2G$\"#5!\"\"" }
}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "sec1:=x->m1*(x-.5)+f4(.5);
" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%sec1Gj+6#%\"xG6\"6$%)operatorG%
&arrowGF(,&*&%#m1G\"\"\",&9$F/$\"\"&!\"\"F4F/F/-%#f4G6#F2F/F(F(F(6#\"
\"!" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "m2:=(f4(a2)-f4(a1))/
(a2-a1);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#m2G$\"+S?B#\\'!#5" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "sec2:=x->m2*(x-a1)+f4(a1);" 
}}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%sec2Gj+6#%\"xG6\"6$%)operatorG%&a
rrowGF(,&*&%#m2G\"\"\",&9$F/%#a1G!\"\"F/F/-%#f4G6#F2F/F(F(F(6#\"\"!" }
}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "a1:=.5;a2:=5.1;" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6#>%#a1G$\"\"&!\"\"" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>%#a2G$\"#^!\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 26 "sec1:=x->m1*(x-.5)+f4(.5);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#
>%%sec1Gj+6#%\"xG6\"6$%)operatorG%&arrowGF(,&*&%#m1G\"\"\",&9$F/$\"\"&
!\"\"F4F/F/-%#f4G6#F2F/F(F(F(6#\"\"!" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 26 "sec2:=x->m2*(x-a1)+f4(a1);" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>%%sec2Gj+6#%\"xG6\"6$%)operatorG%&arrowGF(,&*&%#m2G\"
\"\",&9$F/%#a1G!\"\"F/F/-%#f4G6#F2F/F(F(F(6#\"\"!" }}}{EXCHG {PARA 
202 "> " 0 "" {MPLTEXT 1 -1 20 "f4:=x->(x/sin(x))^2;" }}{PARA 11 "" 1 
"" {XPPMATH 20 "6#>%#f4Gj+6#%\"xG6\"6$%)operatorG%&arrowGF(*&9$\"\"#-%
$sinG6#F-!\"#F(F(F(6#\"\"!" }}}{EXCHG {PARA 202 "> " 0 "" {MPLTEXT 1 
-1 30 "a:=0;seq(f4(a+1.0/n),n=1..20);" }}{PARA 11 "" 1 "" {XPPMATH 20 
"6#>%\"aG\"\"!" }}{PARA 12 "" 1 "" {XPPMATH 20 "66$\"+FHG79!\"*$\"+D8n
(3\"F%$\"+F[(y.\"F%$\"+cj4@5F%$\"+\"oSM,\"F%$\"+G4J45F%$\"+y0$o+\"F%$
\"+\\YA05F%$\"+3a7/5F%$\"+6+M.5F%$\"+!QfF+\"F%$\"+L!=B+\"F%$\"+BZ(>+\"
F%$\"+<Cq,5F%$\"+*z#[,5F%$\"+,JI,5F%$\"+,U:,5F%$\"+U%H5+\"F%$\"+tQ#4+
\"F%$\"+]P$3+\"F%" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 67 "plot([
f4(x),sec1(x),sec2(x)],x=0..2,y=0..2,color=[red,blue,green]);" }}
{PARA 8 "" 1 "" {TEXT -1 35 "Error, (in plot) invalid arguments\n" }}}
{EXCHG {PARA 202 "> " 0 "" {MPLTEXT 1 -1 10 "g:=x->x-1;" }}{PARA 11 "
" 1 "" {XPPMATH 20 "6#>%\"gGj+6#%\"xG6\"6$%)operatorG%&arrowGF(,&9$\"
\"\"F.!\"\"F(F(F(6#\"\"!" }}}{EXCHG {PARA 202 "> " 0 "" {MPLTEXT 1 -1 
15 "seq(i,i=1..10);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6,\"\"\"\"\"#\"\"
$\"\"%\"\"&\"\"'\"\"(\"\")\"\"*\"#5" }}}{EXCHG {PARA 202 "> " 0 "" 
{MPLTEXT 1 -1 15 "seq(n,i=1..10);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6,%
\"nGF#F#F#F#F#F#F#F#F#" }}}{EXCHG {PARA 202 "> " 0 "" {MPLTEXT 1 -1 
15 "seq(n,n=1..10);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6,\"\"\"\"\"#\"\"
$\"\"%\"\"&\"\"'\"\"(\"\")\"\"*\"#5" }}}{EXCHG {PARA 202 "> " 0 "" 
{MPLTEXT 1 -1 17 "seq(n^2,n=1..10);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6
,\"\"\"\"\"%\"\"*\"#;\"#D\"#O\"#\\\"#k\"#\")\"$+\"" }}}{EXCHG {PARA 
202 "> " 0 "" {MPLTEXT 1 -1 17 "seq(1/n,n=1..10);" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6,\"\"\"#F#\"\"##F#\"\"$#F#\"\"%#F#\"\"&#F#\"\"'#F#\"\"(#
F#\"\")#F#\"\"*#F#\"#5" }}}{EXCHG {PARA 202 "> " 0 "" {MPLTEXT 1 -1 
18 "seq(-1/n,n=1..10);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6,!\"\"#F#\"\"
##F#\"\"$#F#\"\"%#F#\"\"&#F#\"\"'#F#\"\"(#F#\"\")#F#\"\"*#F#\"#5" }}}
{EXCHG {PARA 202 "> " 0 "" {MPLTEXT 1 -1 19 "seq(1-1/n,n=1..10);" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6,\"\"!#\"\"\"\"\"##F&\"\"$#F(\"\"%#F*\"
\"&#F,\"\"'#F.\"\"(#F0\"\")#F2\"\"*#F4\"#5" }}}{EXCHG {PARA 202 "> " 
0 "" {MPLTEXT 1 -1 19 "seq(1.0/n,n=1..10);" }}{PARA 12 "" 1 "" 
{XPPMATH 20 "6,$\"#5!\"\"$\"+++++]!#5$\"+LLLLLF($\"+++++DF($\"+++++?F(
$\"+nmmm;F($\"+H9dG9F($\"++++]7F($\"+66666F($\"+++++5F(" }}}{EXCHG 
{PARA 202 "> " 0 "" {MPLTEXT 1 -1 21 "seq(1+1.0/n,n=1..10);" }}{PARA 
12 "" 1 "" {XPPMATH 20 "6,$\"#?!\"\"$\"+++++:!\"*$\"+LLLL8F($\"++++]7F
($\"+++++7F($\"+nmmm6F($\"+Vr&G9\"F($\"++++D6F($\"+66666F($\"+++++6F(
" }}}{EXCHG {PARA 202 "> " 0 "" {MPLTEXT 1 -1 25 "seq(g(1+1.0/n),n=1..
100):" }}}{EXCHG {PARA 202 "> " 0 "" {MPLTEXT 1 -1 49 "f1:=x->2*sin(x)
;f2:=x->cos(x);f3:=x->f1(x)/f2(x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#
>%#f1Gj+6#%\"xG6\"6$%)operatorG%&arrowGF(,$*&\"\"#\"\"\"-%$sinG6#9$F/F
/F(F(F(6#\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#f2Gj+6#%\"xG6\"6$
%)operatorG%&arrowGF(-%$cosG6#9$F(F(F(6#\"\"!" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>%#f3Gj+6#%\"xG6\"6$%)operatorG%&arrowGF(*&-%#f1G6#9$\"
\"\"-%#f2GF/!\"\"F(F(F(6#\"\"!" }}}{EXCHG {PARA 202 "> " 0 "" 
{MPLTEXT 1 -1 55 "plot([f1(x),f2(x),f3(x)],x=0..Pi,y=-2..2,discont=tru
e);" }}{PARA 8 "" 1 "" {TEXT -1 35 "Error, (in plot) invalid arguments
\n" }}}{EXCHG {PARA 202 "> " 0 "" {MPLTEXT 1 -1 26 "seq((Pi/2+1.0/n),n
=1..10);" }}{PARA 12 "" 1 "" {XPPMATH 20 "6,,&*&\"\"#!\"\"%#PiG\"\"\"F
($\"#5F&F(,&*&F%F&F'F(F($\"+++++]!#5F(,&*&F%F&F'F(F($\"+LLLLLF/F(,&*&F
%F&F'F(F($\"+++++DF/F(,&*&F%F&F'F(F($\"+++++?F/F(,&*&F%F&F'F(F($\"+nmm
m;F/F(,&*&F%F&F'F(F($\"+H9dG9F/F(,&*&F%F&F'F(F($\"++++]7F/F(,&*&F%F&F'
F(F($\"+66666F/F(,&*&F%F&F'F(F($\"+++++5F/F(" }}}{EXCHG {PARA 202 "> \+
" 0 "" {MPLTEXT 1 -1 26 "seq((Pi/2-1.0/n),n=1..10);" }}{PARA 12 "" 1 "
" {XPPMATH 20 "6,,&*&\"\"#!\"\"%#PiG\"\"\"F($\"#5F&F&,&*&F%F&F'F(F($\"
+++++]!#5F&,&*&F%F&F'F(F($\"+LLLLLF/F&,&*&F%F&F'F(F($\"+++++DF/F&,&*&F
%F&F'F(F($\"+++++?F/F&,&*&F%F&F'F(F($\"+nmmm;F/F&,&*&F%F&F'F(F($\"+H9d
G9F/F&,&*&F%F&F'F(F($\"++++]7F/F&,&*&F%F&F'F(F($\"+66666F/F&,&*&F%F&F'
F(F($\"+++++5F/F&" }}}{EXCHG {PARA 202 "> " 0 "" {MPLTEXT 1 -1 29 "seq
(f3(Pi/2+1.0/n),n=1..100):" }}}{EXCHG {PARA 202 "> " 0 "" {MPLTEXT 1 
-1 47 "seq(f3(Pi/2+1.0/(n+1))-f3(Pi/2+1.0/n),n=1..10);" }}{PARA 12 "" 
1 "" {XPPMATH 20 "6,$!+7-zwB!\"*$!+I'Q^6#F%$!+_1_c?F%$!+F]nL?F%$!+FGPA
?F%$!*]\\f,#!\")$!*lZ>,#F0$!*;&G4?F0$!*'RU2?F0$!*nrg+#F0" }}}{EXCHG 
{PARA 202 "> " 0 "" {MPLTEXT 1 -1 10 "f:=x->x^2;" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>%\"fGj+6#%\"xG6\"6$%)operatorG%&arrowGF(*$)9$\"\"#\"\"
\"F(F(F(6#\"\"!" }}}{EXCHG {PARA 202 "> " 0 "" {MPLTEXT 1 -1 16 "Limit
(f(x),x=b);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%&LimitG6$\"\"\"/F&%\"
bG" }}}{EXCHG {PARA 202 "> " 0 "" {MPLTEXT 1 -1 35 "a:=1;L:=f(a);epsil
on:=.5;delta:=.7;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"aG\"\"\"" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"LG\"\"\"" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>%(epsilonG$\"\"&!\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 
"6#>%&deltaG$\"\"(!\"\"" }}}{EXCHG {PARA 208 "" 0 "" {TEXT -1 0 "" }}}
{EXCHG {PARA 202 "> " 0 "" {MPLTEXT 1 -1 211 "plot([L,[a-delta,y,y=-10
..10],[a+delta,y,y=-10..10],[a,y,y=-10..10],L-epsilon,L+epsilon,f(x)],
x=-2..2,linestyle=[SOLID,DASH,DASH,SOLID,DASH,DASH,SOLID],color=[PINK,
RED,RED,ORANGE,GREEN,GREEN,BLUE],discont=true);" }}{PARA 8 "" 1 "" 
{TEXT -1 35 "Error, (in plot) invalid arguments\n" }}}{EXCHG {PARA 0 "
> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 
"" }}}{EXCHG {PARA 208 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 208 "" 0 
"" {TEXT -1 0 "" }}}{EXCHG {PARA 208 "" 0 "" {TEXT -1 0 "" }}}{PARA 
209 "" 0 "" {TEXT -1 0 "" }}{PARA 209 "" 0 "" {TEXT -1 0 "" }}}{MARK "
7 1 0" 0 }{VIEWOPTS 1 1 0 3 2 1804 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 
}