{VERSION 6 0 "IBM INTEL NT" "6.0" } {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 Output" 2 20 "" 0 1 0 0 255 1 0 0 0 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 "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 Output" -1 12 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }1 3 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Maple Plot" 0 13 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }3 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "R3 Font 0" -1 256 1 {CSTYLE "" -1 -1 "Helvetica" 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 }{PSTYLE "R3 Font 2" -1 257 1 {CSTYLE " " -1 -1 "Courier" 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 }} {SECT 0 {EXCHG {PARA 0 "" 0 "" {TEXT -1 37 "Math 251. \+ Quiz 4." }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "with(plots):" }}} {EXCHG {PARA 0 "" 0 "" {TEXT -1 123 "Problem 1. Use Taylor's series fo rmula to find the first three non-zero terms for the Maclaurin series \+ for 1/(sqrt(1-x^2))." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "tay lor(1/sqrt(1-x^2),x=0,5);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#++%\"xG\" \"\"\"\"!#F%\"\"#F(#\"\"$\"\")\"\"%-%\"OG6#F%\"\"'" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 117 "Problem 2. Use Taylor's series formula to find t he first three non-zero terms for the Maclaurin series for arcsin(x). " }}{PARA 0 "" 0 "" {TEXT -1 60 "Notice the relationship between arcsi n(x) and 1/sqrt(1-x^2)." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 " taylor(arcsin(x),x=0,7);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#++%\"xG\" \"\"F%#F%\"\"'\"\"$#F(\"#S\"\"&-%\"OG6#F%\"\"(" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 11 "Problem 3. \+ " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "taylor(1/(1+x^2),x=0,7) ;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#+-%\"xG\"\"\"\"\"!!\"\"\"\"#F%\" \"%F'\"\"'-%\"OG6#F%\"\")" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "taylor(arctan(x),x=0,7);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#++%\"x G\"\"\"F%#!\"\"\"\"$F(#F%\"\"&F*-%\"OG6#F%\"\"(" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 26 "taylor(arctan(x)/x,x=0,7);" }}{PARA 11 "" 1 " " {XPPMATH 20 "6#++%\"xG\"\"\"\"\"!#!\"\"\"\"$\"\"##F%\"\"&\"\"%-%\"OG 6#F%\"\"'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 37 "evalf(int(1-1/ 3*x^2+1/5*x^4,x=0..2));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+666\"R# !\"*" 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"convert(%,polynom);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,(*$)% \"xG\"\"#\"\"\"F(*&#F(\"\"'F(*$)F&F+F(F(!\"\"*&#F(\"$?\"F(*$)F&\"#5F(F (F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 31 "p10:=x->x^2-1/6*x^6+ 1/120*x^10;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$p10Gf*6#%\"xG6\"6$%) operatorG%&arrowGF(,(*$)9$\"\"#\"\"\"F1*&#F1\"\"'F1*$)F/F4F1F1!\"\"*&# F1\"$?\"F1*$)F/\"#5F1F1F1F(F(F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "int(p10(x),x=0..0.5);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+n C5[T!#6" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "evalf(int(sin(x^ 2),x=0..0.5));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+FC5[T!#6" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "p6:=x->x^2-1/6*x^6;" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%#p6Gf*6#%\"xG6\"6$%)operatorG%&arrow GF(,&*$)9$\"\"#\"\"\"F1*&#F1\"\"'F1*$)F/F4F1F1!\"\"F(F(F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "int(p6(x),x=0..0.5);" }}{PARA 11 " " 1 "" {XPPMATH 20 "6#$\"+wa1[T!#6" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "p2:=x->x^2;" 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