{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 }{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 "Title " 0 18 1 {CSTYLE "" -1 -1 "" 1 18 0 0 0 0 0 1 1 0 0 0 0 0 0 0 }3 0 0 -1 12 12 0 0 0 0 0 0 19 0 }} {SECT 0 {EXCHG {PARA 18 "" 0 "" {TEXT -1 38 "l'hopital's rule: why it \+ works (zoom!)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "plot([x^2- 1,x^3-1],x=0..2);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 33 "plot([ x^2-1,x^3-1],x=0.99..1.01);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 83 "plot([x^3-1,x^2-1,0.03,0.02],x=1.0..1.01,\naxes=boxed,color=[red,b lue,green,green]);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 66 "ratio of tw o functions is just the ratio of their limiting slopes:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 54 "Limit((x^3-1)/(x^2-1),x=1)=limit((x ^3-1)/(x^2-1),x=1);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}} }{MARK "0 0 0" 38 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }