{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 Output" 2 20 "" 0 1 0 0 255 1 0 0 0 0 0 0 0 0 0 1 } {CSTYLE "" -1 256 "" 1 14 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 257 "" 1 14 0 0 0 0 0 1 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 258 "" 0 1 0 0 0 0 2 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 259 "" 0 1 0 0 0 0 1 1 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 "" 1 14 0 0 0 0 0 1 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 262 "" 0 1 0 0 0 0 1 1 0 0 0 0 0 0 0 1 }{PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "Heading 1" 0 3 1 {CSTYLE "" -1 -1 "" 1 18 0 0 0 0 0 1 0 0 0 0 0 0 0 1 }1 0 0 0 8 4 0 0 0 0 0 0 -1 0 }{PSTYLE "Head ing 2" 3 4 1 {CSTYLE "" -1 -1 "" 1 14 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }0 0 0 -1 8 2 0 0 0 0 0 0 -1 0 }{PSTYLE "Heading 3" 4 5 1 {CSTYLE "" -1 -1 "" 1 12 0 0 0 0 1 0 0 0 0 0 0 0 0 1 }0 0 0 -1 0 0 0 0 0 0 0 0 -1 0 }{PSTYLE "Maple Output" 0 11 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }3 3 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "Maple Plot" 0 13 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }3 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }} {SECT 0 {EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }{TEXT 256 0 "" }{TEXT 257 22 "Solution to Problem 1." }}}{SECT 0 {PARA 5 "" 0 "" {TEXT 258 10 "Problem 1:" }{TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 27 "Using Si mpson's rule, find " }{XPPEDIT 18 0 "int(exp(x^2),x = 0 .. 1);" "6#-%$ intG6$-%$expG6#*$%\"xG\"\"#/F*;\"\"!\"\"\"" }{TEXT -1 26 " to within a n accuracy of " }{XPPEDIT 18 0 "10^(-5);" "6#)\"#5,$\"\"&!\"\"" } {TEXT -1 2 " ." }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "fd:=diff(e xp(x^2),x$4);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#fdG,(-%$expG6#*$)% \"xG\"\"#\"\"\"\"#7*&F*F-F&F-\"#[*&)F+\"\"%F-F&F-\"#;" }}}}{EXCHG {PARA 11 "" 1 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 35 "plot(abs(fd),x = 0..1, y = 0..300);" }}{PARA 13 "" 1 "" {GLPLOT2D 344 123 123 {PLOTDATA 2 "6%-%'CURVESG6$7S7$\"\"!$\"#7F(7$$\" 1nmm;arz@!#<$\"1b^otr8F17$$\"1+ +D1J:w=FD$\"1V3_&zb+U\"F17$$\"1LLL3En$4#FD$\"1vSZf\"=oZ\"F17$$\"1nm;/R E&G#FD$\"1(zfu?[I`\"F17$$\"1+++D.&4]#FD$\"1e[?]Rs.;F17$$\"1+++vB_F17$$\"1LLLLY.KNFD$\"1K!\\\\ vFg1#F17$$\"1++D\"o7Tv$FD$\"1EQ)G%H2(>#F17$$\"1LLL$Q*o]RFD$\"1dkBvm*RK #F17$$\"1++D\"=lj;%FD$\"1l0:J])fZ#F17$$\"1++vV&RY2aFD$\"1/M!HF26n$F17$$\"1mm;zXu9cFD$\"1wAra=qORF17$$\"1+++]y))G eFD$\"1Em(HYgcB%F17$$\"1****\\i_QQgFD$\"1jefoCZaXF17$$\"1***\\7y%3TiFD $\"1xS\"f7p**)[F17$$\"1****\\P![hY'FD$\"1u\"*otE^'H&F17$$\"1LLL$Qx$omF D$\"1Q\"yb-w^p&F17$$\"1+++v.I%)oFD$\"1OVpWV,fhF17$$\"1mm\"zpe*zqFD$\"1 [!4%\\V[;mF17$$\"1+++D\\'QH(FD$\"1WRw\"=Y3;(F17$$\"1KLe9S8&\\(FD$\"1K] R]Z7>xF17$$\"1***\\i?=bq(FD$\"1L%[x/!*\\N)F17$$\"1LLL3s?6zFD$\"1x2*3TS K.*F17$$\"1++DJXaE\")FD$\"17D'*Qn34)*F17$$\"1nmmm*RRL)FD$\"1)HlIb9E1\" !#87$$\"1mm;a<.Y&)FD$\"1E#H&G2'R:\"F`x7$$\"1LLe9tOc()FD$\"1;YOk@5`7F`x 7$$\"1+++]Qk\\*)FD$\"10s_&GUCN\"F`x7$$\"1LL$3dg6<*FD$\"17b[9*ppZ\"F`x7 $$\"1mmmmxGp$*FD$\"1C8'H-b*)f\"F`x7$$\"1++D\"oK0e*FD$\"1*3WrGr6u\"F`x7 $$\"1++v=5s#y*FD$\"1(eI3([?!*=F`x7$$\"\"\"F($\"1u)G'*=%*e1#F`x-%'COLOU RG6&%$RGBG$\"#5!\"\"F(F(-%+AXESLABELSG6$Q\"x6\"Q\"yFd[l-%%VIEWG6$;F(Fe z;F($\"$+$F(" 1 2 0 1 10 0 2 9 1 4 2 1.000000 45.000000 45.000000 0 0 "Curve 1" }}}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 45 "From the graph, it i s safe to choose M = 250." }}{PARA 0 "" 0 "" {TEXT -1 59 "Substitute t his value in the error formula and solve for n." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "" 0 " " {XPPEDIT 18 0 "error:=(b-a)^5*M/(180*n^4);" "6#%#%?G" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 39 "n:=((1-0)^5*250/(180.0*10^(-5)))^(1 /4);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"nG$\"+wp[I>!\")" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 17 "Let n = 20. Why?" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }} {PARA 0 "" 0 "" {TEXT 259 6 "Check:" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "with(student):" } }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 43 "est:=evalf(simpson(exp(x^2 ), x = 0..1,20));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$estG$\"+DOli9! \"*" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 35 "act:=evalf(int(exp(x^2),x = 0..1));" }}{PARA 11 " " 1 "" {XPPMATH 20 "6#>%$actG$\"+Y " 0 " " {MPLTEXT 1 0 15 "Error:=act-est;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6# >%&ErrorG$!%z=!\"*" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }{TEXT 260 0 "" }{TEXT 261 19 "Problem 2 Solution:" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 27 "Using Simpson's rule, find " } {XPPEDIT 18 0 "int(exp(cos(x)),x = 0 .. Pi);" "6#-%$intG6$-%$expG6#-%$ cosG6#%\"xG/F,;\"\"!%#PiG" }{TEXT -1 26 " to within an accuracy of " } {XPPEDIT 18 0 "10^(-7);" "6#)\"#5,$\"\"(!\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "k:=exp(cos(x));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"kG-%$expG6#-%$cosG6#%\"xG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "fd:=diff(exp(cos(x)),x$4);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#fdG,,*&-%$cosG6#%\"xG\"\"\"-%$expG6#F'F+F+*&)-%$sinG F)\"\"#F+F,F+!\"%*&)F'F3F+F,F+\"\"$*(F'F+F0F+F,F+!\"'*&)F1\"\"%F+F,F+F +" }}}{EXCHG {PARA 11 "" 1 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 35 "plot(abs(fd),x = 0..Pi, y = 0..15);" }}{PARA 13 "" 1 "" {GLPLOT2D 344 123 123 {PLOTDATA 2 "6%-%'CURVESG6$7bp7$\"\"!$\"1=O QJFJ(3\"!#97$$\"1*pSjTA(f&)!#=$\"1.94[S+(3\"F+7$$\"1S\"oK[W>r\"!#<$\"1 dkou#yg3\"F+7$$\"15A!\\s;zc#F5$\"1_NBSi`%3\"F+7$$\"1zi`m*))QU$F5$\"1A, MD$zB3\"F+7$$\"1>W!)\\M$e8&F5$\"1!3(=B\"Hi2\"F+7$$\"1fD2LzxZoF5$\"12&Q ,m\\w1\"F+7$$\"1b4U:a)o#)*F5$\"1;5g'fBq/\"F+7$$\"1Npx*G*f!G\"!#;$\"1I, us.O>5F+7$$\"1A&zO3Jch\"FT$\"1EoM$QZ@!)*!#:7$$\"15@exGm]>FT$\"1=RC#QD2 L*Ffn7$$\"1i1@Ffn7$$\" 15lN\"oP>c&FT$\"10!QEp\"f)H\"Ffn7$$\"1PRr4)3T*eFT$\"1dz&4:@F6&FT7$$\"1 c#[$=&G&zfFT$\"1z_M^5(*HJFT7$$\"1uD)pA[\\1'FT$\"1&\\Yh%orm6FT7$$\"1`69 aJI'3'FT$\"1-8!>&)[3z'F57$$\"1L(*H\"3ew5'FT$\"1>'*om.hF>F57$$\"18$e%3I ,HhFT$\"1VNv2=PAHF57$$\"1#*ohNzO]hFT$\"1u\"G5vB*exF57$$\"1^S$**yxI>'FT $\"1#p:Nw/\"R:1FmS'FT$\"1Rp iCS%)okFT7$$\"1#[)yykYxlFT$\"1xPOLF895Ffn7$$\"1x&GAQ<%yoFT$\"1X?!H#e_M ;Ffn7$$\"1s'ocGo$zrFT$\"1(*>8sx&y@#Ffn7$$\"11Y\"Hsn\"=vFT$\"1(Q\"f2/AE GFfn7$$\"1Q0;gr'p&yFT$\"1^=,!HZ)zLFfn7$$\"1$)pWSx:(>)FT$\"1d;xsj(y(QFf n7$$\"1GMt?$[t`)FT$\"1L)3k$e.;VFfn7$$\"1#p30k@I>*FT$\"19q__#G())\\Ffn7 $$\"1S7\\HeV)y*FT$\"1*RfRN*\\0aFfn7$$\"1/)of$QC95Ffn$\"1QlKLV(*obFfn7$ $\"1$[))*)3W'\\5Ffn$\"1qu2=E!Gn&Ffn7$$\"1M<(yTQY1\"Ffn$\"1o*G*QRf*p&Ff n7$$\"1%)\\vYFjz5Ffn$\"1/eb(3glr&Ffn7$$\"1N#Qc2FY4\"Ffn$\"1kW)zZ(*Rs&F fn7$$\"1'[@XS@'46Ffn$\"1tWDy`@AdFfn7$$\"1]&zEM0X9\"Ffn$\"19'=Qv-Uo&Ffn 7$$\"19w$3G*Qz6Ffn$\"1#oz4yuAg&Ffn7$$\"1\\L'pZn-@\"Ffn$\"1zMe_km'\\&Ff n7$$\"1%3*3tc9T7Ffn$\"11kFP1Fj`Ffn7$$\"1y0DBA!*38Ffn$\"1'>&3%G:())\\Ff n7$$\"1kE.#[AMP\"Ffn$\"1n]ud50_XFfn7$$\"1a@X.EuS9Ffn$\"1P4Hl[oUSFfn7$$ \"1WF)**[jD]\"Ffn$\"1(=!*R)\\o\\NFfn7$$\"1hw\"ymX#p:Ffn$\"1$)*zP%)3C,$ Ffn7$$\"1xM!*4(4&Q;Ffn$\"1\\2$zQzyY#Ffn7$$\"1DL:iU!))p\"Ffn$\"15H-i)*p J=Ffn$\"1SrJ!)oV V6Ffn7$$\"1fb7wY,(*=Ffn$\"1-uqD!4Vx(FT7$$\"1N5'zg%pg>Ffn$\"1L)Q:D3$*o% FT7$$\"1pJ8:.SJ?Ffn$\"1!ev7mt'z\"FT7$ $\"1M>YEk;j?Ffn$\"1-<'[Q.\">kF57$$\"1ETHaz5r?Ffn$\"1Oro_ebKPF57$$\"1k\\)G@Ffn$\"1T\"o9z%=)R\"FT7$$\"1=!fh umF;#Ffn$\"1%p[IR()oH#FT7$$\"1bk3@YBCAFfn$\"1f\"*yN/w!o$FT7$$\"1/bQ'FT7$$\"11()=U!z`[#Ffn$\"1)G*of$py$oFT7$$\"1kHHd#HIb#F fn$\"17p!\\0)pbrFT7$$\"1_r&[X%==EFfn$\"1TOe\\:QUtFT7$$\"1K-%\\0:[o#Ffn $\"1SOt]eRVuFT7$$\"1gN,?R*3v#Ffn$\"1#>]Yu\"Q![(FT7$$\"1/0LMNh6GFfn$\"1 m'otZ1\"yuFT7$$\"1$oUX107)GFfn$\"1WTV(f1;X(FT7$$\"146xe&[M%HFfn$\"1x') em!o&>uFT7$$\"1.6)e58)4IFfn$\"1['=y.PvQ(FT7$$\"1t2RXCLtIFfn$\"1G[%[=;g O(FT7$$\"1++X]EfTJFfn$\"1Z)GM#))edtFT-%'COLOURG6&%$RGBG$\"#5!\"\"F(F(- %+AXESLABELSG6$Q\"x6\"Q\"yF^gl-%%VIEWG6$;F($\"+aEfTJ!\"*;F($\"#:F(" 1 2 0 1 10 0 2 9 1 4 2 1.000000 45.000000 45.000000 0 0 "Curve 1" }}}} {EXCHG {PARA 0 "" 0 "" {TEXT -1 44 "From the graph, it is safe to choo se M = 11." }}{PARA 0 "" 0 "" {TEXT -1 59 "Substitute this value in th e error formula and solve for n." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }} {PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "" 0 "" {XPPEDIT 18 0 "error:=(b-a)^5*M/(180*n^4);" "6#%#%?G" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 39 "n:=((Pi-0)^5*11/(180.0*10^(-7)))^(1/4);" }}{PARA 11 " " 1 "" {XPPMATH 20 "6#>%\"nG,$*$)*$)%#PiG\"\"&\"\"\"#F,\"\"%F,$\"+[T&f z#!\")" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "evalf(%);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+p:Tp6!\"(" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 18 "Let n = 118. Why?" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }} {PARA 0 "" 0 "" {TEXT 262 6 "Check:" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "with(student):" } }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 44 "est:=evalf(simpson(exp(x^2 ), x = 0..1,118));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$estG$\"+[ " 0 "" {MPLTEXT 1 0 35 "act:=evalf(int(exp(x^2),x = 0..1));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$actG$\"+Y " 0 "" {MPLTEXT 1 0 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "Error:=act-e st;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%&ErrorG$!\"#!\"*" }}}{PARA 0 "" 0 "" {TEXT -1 77 "_________________________________________________ ____________________________" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 172 "MSIP Grant #P120A80089-98: \"Three Urban Calc ulus Reform programs: Adopting the Best\" 1998-2001, MSEIP Grant #P120 A010031: \"Four Colleges: Calculus + Enhancements\" 2001-04" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{MARK "34 0" 0 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }