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od;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$!%n;!\"% " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$!# " 0 "" {MPLTEXT 1 0 7 "d := 3:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "Digits := d:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "unassign('n'):" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "unassign( 's'):" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 7 "s := 0:" }}{PARA 0 "> " 0 " " {MPLTEXT 1 0 23 "for n from 1 to 10^d do" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 31 "s := evalf(s + evalf(1/n)): od:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 2 "s;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"$;'!\"#" }}} {EXCHG {PARA 0 "" 0 "" {TEXT -1 31 "\254\333\270\373\251\363\244@\255 \323\257u\245\277\252\272\246\254\300\304\257\305\274\306, \250\322 \246p " }{XPPEDIT 18 0 "Sum(1/n^2,n=1..infinity)=(Pi^2/6)" "/-%$SumG6$ *&\"\"\"F'*$%\"nG\"\"#!\"\"/F);F'%)infinityG*&%#PiGF*\"\"'F+" }{TEXT -1 1 " " }}{PARA 0 "" 0 "" {TEXT -1 37 "\274\306\255\310\252\272\246 \364\255p\300\263\270\323\300H\265\333\272\353\275T\253\327\252\272 \264\243\260\252\246\323\267\307\275T." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "evalf(Pi^2/6, 10);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6 #$\"+oS$\\k\"!\"*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 7 "d := 4: " }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "Digits := d:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "unassign('n'):" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "unassign('s'):" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 7 "s := 0:" }} {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "for n from 1 to 10^d do" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 33 "s := evalf(s + evalf(1/n^2)): od:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 2 "s;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"% D;!\"$" }}}}{SECT 1 {PARA 3 "" 0 "" {TEXT 262 10 "\263t\253\327\252 \272\304v\301\311" }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 12 "Lecture 13: \+ " }{XPPEDIT 18 0 "sin(1/x)" "-%$sinG6#*&\"\"\"F&%\"xG!\"\"" }{TEXT -1 19 " when x very large " }{XPPEDIT 18 0 "Limit(x*sin(1/x), x=infinity) = 1" "/-%&LimitG6$*&%\"xG\"\"\"-%$sinG6#*&F(F(F'!\"\"F(/F'%)infinityG F(" }{TEXT -1 19 " same thing to say" }{XPPEDIT 18 0 " Limit(sin(1/x) /(1/x), x=infinity)= 1" "/-%&LimitG6$*&-%$sinG6#*&\"\"\"F+%\"xG!\"\"F+ *&F+F+F,F-F-/F,%)infinityGF+" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 8 "Example " }{XPPEDIT 18 0 "Limit(x^2/(x*sqrt(x^2+ Pi) -100), x=infinity) = 1" "/-%&LimitG6$*&%\"xG\"\"#,&*&F'\"\"\"-%%sq rtG6#,&*$F'F(F+%#PiGF+F+F+\"$+\"!\"\"F3/F'%)infinityGF+" }{TEXT -1 2 " " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 45 "limit(x^2/(x*sqrt(x^2 +Pi) -100), x=infinity);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"\"" }} }{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "X := plot(sin(1/x), x=3..10 ):" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 38 "Y := plot(1/x, x=3..10, color =[blue]):" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "display(\{X,Y\});" }} {PARA 13 "" 1 "" {INLPLOT "6&-%'CURVESG6$7S7$$\"\"$\"\"!$\"1LLLLLLLL!# ;7$$\"1mm;z+e_J!#:$\"1.>or]+sJF-7$$\"1M$3->R`G$F1$\"1I**\\Ud#Q/$F-7$$ \"1nmT&pSYV$F1$\"1V$[')p7:\"HF-7$$\"1nm\"z'=$\\e$F1$\"1Z\\%=H`%*y#F-7$ $\"1M$3Ft3Xt$F1$\"143$\\PGxn#F-7$$\"1n;aLc=tQF1$\"10@HYS&=e#F-7$$\"1+] (=`xn,%F1$\"1D?*4%yb*[#F-7$$\"1n;ay/GlTF1$\"1#)*y+r)z+CF-7$$\"1+]PurI8 VF1$\"1XI_TmS=BF-7$$\"1ML$e#3dlWF1$\"1\\o*zOb$RAF-7$$\"1nm\"Ht%o*f%F1$ \"1\"o&pX?1u@F-7$$\"1,+]F_m]ZF1$\"1?s]h$o\\5#F-7$$\"1++]icE-\\F1$\"17Z yHJ()R?F-7$$\"1,+]s2O[]F1$\"1/*4)**4%3)>F-7$$\"1n;aG\"H5=&F1$\"1;3=n%= ,$>F-7$$\"1LL$ej%yQ`F1$\"1G\"HL[&3t=F-7$$\"1MLLVUUsaF1$\"1faV1PMF=F-7$ $\"1+](o()yyi&F1$\"1x1&fPoox\"F-7$$\"1LLLoD[ldF1$\"1$3w:>gWt\"F-7$$\"1 ,](oibk\"fF1$\"1!zUB8,-p\"F-7$$\"1,]i!o<-1'F1$\"1bhAVd5];F-7$$\"1ML3-$ =-@'F1$\"1d+`_$\\-h\"F-7$$\"1M$3xplzM'F1$\"194E>yIv:F-7$$\"1nm\"H([a' \\'F1$\"1a#\\\\vz#R:F-7$$\"1m;ayo(3l'F1$\"1\"Qnn8hN]\"F-7$$\"1,]7VLA&y 'F1$\"1B'f%Q3zt9F-7$$\"1nmT07KIpF1$\"1*z,IcMHW\"F-7$$\"1+++&\\@-3(F1$ \"1$*)=E>&Q79F-7$$\"1++v$opoA(F1$\"1A9(\\'\\s$Q\"F-7$$\"1,](oMf(otF1$ \"1yF1$\"1?()pYU$*y7F-7$$\"1m;a)3rf&zF1$\"1=a:*e\"F-7$$\"1LL$e/Xy`)F1$\"1\"z*)ztb7< \"F-7$$\"1,](=<\"e)o)F1$\"1P<1,f$4:\"F-7$$\"1ommwzvL))F1$\"1*HUA0@?8\" F-7$$\"1nm\"zAAA)*)F1$\"1F%[%*F1$\"1L7+nAfh5F-7$$ \"1nmmO9]e&*F1$\"1$[\"R)4*=Y5F-7$$\"1,](o(GP1(*F1$\"1T_ii4DI5F-7$$\"1, ]78Z!z%)*F1$\"10q?JWW:5F-7$$\"#5F*$\"1+++++++5F--%'COLOURG6&%$RGBGF*F* $\"*++++\"!\")-F$6$7S7$F($\"1A:'z'p%>F$F-7$F/$\"1x4&o`z!>JF-7$F5$\"1c` Q$)=/(*HF-7$F:$\"1wYaEBbqGF-7$F?$\"1dvHz*=Mv#F-7$FD$\"1aGIDI%ek#F-7$FI $\"1k7AG_E`DF-7$FN$\"1.;)zq?RY#F-7$FS$\"1f\">T2-yP#F-7$FX$\"1H)Q:H$p(H #F-7$Fgn$\"19'RZ.'o?AF-7$F\\o$\"1b2vMh(p:#F-7$Fao$\"1XI7_zX*3#F-7$Ffo$ \"19KRLdvD?F-7$F[p$\"1itVxD\"z'>F-7$F`p$\"1!**y9!o:=>F-7$Fep$\"1!oN>(> :i=F-7$Fjp$\"1#*o-T4><=F-7$F_q$\"1?[WiI`n " 0 "" {MPLTEXT 1 0 0 "" }}}}{MARK "2" 0 }{VIEWOPTS 1 1 0 1 1 1803 }