{VERSION 2 3 "IBM INTEL NT" "2.3" } {USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 0 1 255 0 0 1 0 1 0 0 1 0 0 0 0 }{CSTYLE "2D Math" -1 2 "Times" 0 1 116 111 127 0 0 0 2 0 0 0 0 0 0 }{CSTYLE "2D Output" 2 20 "" 0 1 0 0 255 1 0 0 0 0 0 0 0 0 0 } {PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "" 0 1 0 0 112 0 0 0 0 0 0 0 0 0 0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "Maple Output" 0 11 1 {CSTYLE "" -1 -1 "" 0 1 150 0 172 0 0 0 0 0 0 0 0 0 0 }1 3 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "Title" 0 18 1 {CSTYLE "" -1 -1 "" 1 18 104 168 230 0 0 1 1 0 0 0 0 0 0 }3 0 0 -1 12 12 0 0 0 0 0 0 19 0 }{PSTYLE "Author" 0 19 1 {CSTYLE "" -1 -1 "" 0 1 197 191 130 0 0 0 0 0 0 0 0 0 0 }3 0 0 -1 8 8 0 0 0 0 0 0 -1 0 }} {SECT 0 {EXCHG {PARA 18 "" 0 "top_s03_1" {TEXT -1 41 "3.1 The Limit o f the Difference Quotient" }}{PARA 19 "" 0 "" {TEXT -1 25 "Art Belmont e, Summer 1996" }}{PARA 0 "" 0 "" {TEXT -1 63 "These are the shaded gr ay examples which appear in Section 3.1." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 68 "restart; f:=x->x^3 - 8*x;\nLimit((f(2+h) - f(2)) / h, h=0); value(\");" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"fG:6#%\"xG6\" 6$%)operatorG%&arrowGF(,&*$9$\"\"$\"\"\"F.!\")F(F(" }}{PARA 11 "" 1 " " {XPPMATH 20 "6#-%&LimitG6$*&,(*$,&\"\"#\"\"\"%\"hGF+\"\"$F+!\")F+F,F .F+F,!\"\"/F,\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"%" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "y:=4*(x - 2) - 8;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"yG,&%\"xG\"\"%!#;\"\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "plot(\{y, f(x)\}, x=0..4);" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "plot(\{y, f(x)\}, x=1.8..2.2 );" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 61 "Limit((f(x+h) - f(x)) / h, h=0);\nDf:=value(\"); subs(x=2, Df);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%&LimitG6$*&,(*$,&%\"xG\"\"\"%\"hGF+\"\"$F+F,!\")*$F*F -!\"\"F+F,F0/F,\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#DfG,&!\")\" \"\"*$%\"xG\"\"#\"\"$" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"%" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "diffq:=(f(x+h) - f(x)) / h; " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%&diffqG*&,(*$,&%\"xG\"\"\"%\"hGF *\"\"$F*F+!\")*$F)F,!\"\"F*F+F/" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "simplify(diffq);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,**$%\"xG \"\"#\"\"$*&F%\"\"\"%\"hGF)F'*$F*F&F)!\")F)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{MARK "0 2 0" 62 }{VIEWOPTS 1 1 0 1 1 1803 }