{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 } {PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 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 "Heading 1" 0 3 1 {CSTYLE "" -1 -1 "" 1 18 0 0 0 0 0 1 0 0 0 0 0 0 0 0 }1 0 0 0 8 4 0 0 0 0 0 0 -1 0 }{PSTYLE "Heading 2" 3 4 1 {CSTYLE "" -1 -1 "" 1 14 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }0 0 0 -1 8 2 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 0 } 3 3 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 11 12 1 {CSTYLE "" -1 -1 " " 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }1 0 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 0 }3 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }} {SECT 0 {PARA 4 "" 0 "" {TEXT -1 10 "P\370\355klad 4." }}{PARA 0 "" 0 "" {TEXT -1 33 "Necht\264je zadan\341 funkce f : y = " }{XPPEDIT 18 0 "(2^x-1)/x;" "6#*&,&)\"\"#%\"xG\"\"\"F(!\"\"F(F'F)" }{TEXT -1 39 " \+ . Vypo\350teme jej\355 limitu v bod\354 x = 0." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 74 "Z defini\350n\355ho oboru funkce vid\355me, \236e x = 0 nepat\370\355 do defini\350n\355ho obo ru." }}{PARA 0 "" 0 "" {TEXT -1 82 "Abychom z\355skali p\370edstavu o \+ pr\371b\354hu zadan\351 funkce, nech\341me si vykreslit jej\355 graf. " }}{PARA 0 "" 0 "" {TEXT -1 115 "Proto\236e n\341s zaj\355m\341 chov \341n\355 funkce v okol\355 nuly, zobraz\355me si graf tak\351 podrobn \354ji pro x z intervalu (-0.01..0.01)." }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }{MPLTEXT 1 0 16 "f:=x->(2^x-1)/x;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"fGf*6#%\"xG6\"6$%)operatorG%&arrowGF(*&,&)\"\"#9$\" \"\"F1!\"\"F1F0F2F(F(F(" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 13 "Grafy \+ funkce:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 74 "plot(f(x),x=-10..10,axes font=[TIMES,ROMAN,15],labelfont=[TIMES,ROMAN,15]);" }}{PARA 13 "" 1 " " {GLPLOT2D 400 300 300 {PLOTDATA 2 "6&-%'CURVESG6$7Y7$$!#5\"\"!$\"3s* ****\\PM-***!#>7$$!3!pmmm\"p0k&*!#<$\"3*GuV?4+U/\"!#=7$$!3uKL$3\"F47$$!3OLL$3i.9!zF1$\"3[>;x-XIg7F47$$!3fmm;/R=0vF1$ \"3B3vdz\"y]K\"F47$$!3k++]P8#\\4(F1$\"3IcGZo'[\"*R\"F47$$!3Kmm;/siqmF1 $\"3Oyg^FRR%[\"F47$$!3Q****\\(y$pZiF1$\"3!=l\"R$zE&z:F47$$!3jKLL$yaE\" eF1$\"3%oV&H'zv(*o\"F47$$!3s%HaF1$\"3-)\\UQAi!*z\"F47$$!3]***** *\\$*4)*\\F1$\"3?&*o'pNa\"Q>F47$$!3o******\\_&\\c%F1$\"3kP2vxA0)4#F47$ $!3%)******\\1aZTF1$\"3-:XW*pC]F#F47$$!3Imm;/#)[oPF1$\"3))30()el')eCF4 7$$!3%HLLL=exJ$F1$\"31ho(ol-=r#F47$$!3lKLLL2$f$HF1$\"3/(p(3(o\")4'HF47 $$!3%)****\\PYx\"\\#F1$\"3e>$4(Gnq*H$F47$$!3gLLLL7i)4#F1$\"3UF`\")>s[_ OF47$$!3o)***\\P'psm\"F1$\"3ndtq99U4TF47$$!3?****\\74_c7F1$\"3_nRIcJWF YF47$$!3M:LL$3x%z#)F4$\"3w\">`U'\\7u_F47$$!3()HLL3s$QM%F4$\"3m-.XkdE&) fF47$$!3]^omm;zr)*!#?$\"3f+f\"H96y!pF47$$\"3fVLLezw5VF4$\"3!*eXnBLOy!) 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" }}{PARA 0 "" 0 "" {TEXT -1 0 "" } {MPLTEXT 1 0 23 "sez1:=[seq(i, i=2..7)];" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%sez1G7(\"\"#\"\"$\"\"%\"\"&\"\"'\"\"(" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 24 "sez2:=[seq(8-i,i=1..6)];" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%sez2G7(\"\"(\"\"'\"\"&\"\"%\"\"$\"\"#" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 47 "hodn:=[seq(-0.1^i, i=sez1),seq(0.1^ i, i=sez2)];" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%hodnG7.$!\"\"!\"#$F '!\"$$F'!\"%$F'!\"&$F'!\"'$F'!\"($\"\"\"F2$F4F0$F4F.$F4F,$F4F*$F4F(" } }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 35 "seq('f'(i)=evalf(f(i),15), i=hodn);" }}{PARA 12 "" 1 "" {XPPMATH 20 "6./-%\"fG6#$!\"\"!\"#$\"0+k Hc/v!p!#:/-F%6#$F(!\"$$\"0+qa4q!HpF,/-F%6#$F(!\"%$\"0++YeJ7$pF,/-F%6#$ F(!\"&$\"0++IyZ9$pF,/-F%6#$F(!\"'$\"0+++Sp9$pF,/-F%6#$F(!\"($\"0+++gr9 $pF,/-F%6#$\"\"\"FM$\"0++++s9$pF,/-F%6#$FTFF$\"0+++?u9$pF,/-F%6#$FTF?$ \"0+++$e\\JpF,/-F%6#$FTF8$\"0++!Q?rJpF,/-F%6#$FTF1$\"0++eiuQ$pF,/-F%6# $FTF)$\"0+?n0]b&pF," }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 82 "Z grafu i \+ tabulky m\371\236eme p\370edpokl\341dat , \236e hodnota limity bude p \370ibli\236n\354 0, 6931 ." }}{PARA 0 "" 0 "" {TEXT -1 24 "P\370esnou hodnotu ur\350\355me :" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "with(stu dent,Limit):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "Limit(f(x), x=0):%=value(%);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/-%&LimitG6$*&,&) \"\"#%\"xG\"\"\"F,!\"\"F,F+F-/F+\"\"!-%#lnG6#F*" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 13 "evalf(ln(2));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+1=ZJp!#5" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{MARK "0 0" 0 } {VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }