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Zaj\355mav\354j\232\355 to ale bude v bod\354 -0,5:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "limit(f(x), x=-.5);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"\"\"%*un definedG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "limit(f(x), x=- .5, left);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$!\"\"%)infinityG" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "limit(f(x), x=-.5, right);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"\"\"%)infinityG" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 272 47 "I v tomto p\370\355pad\354 snad m\371\236eme p o\350\355ta\350i v\354\370it..." }}}}{SECT 0 {PARA 259 "" 0 "" {TEXT 273 2 "2." }{TEXT 275 1 " " }{XPPEDIT 276 0 "limit(((1+x)*(1+2*x)*(1+3 *x)-1)/x, x=0)" "6#-%&limitG6$*&,&*(,&\"\"\"F*%\"xGF*F*,&F*F**&\"\"#F* F+F*F*F*,&F*F**&\"\"$F*F+F*F*F*F*F*!\"\"F*F+F2/F+\"\"!" }{TEXT 274 21 " (Demidovi\350 412)." }}{EXCHG {PARA 0 "" 0 "" {TEXT 277 7 "\330e \232en\355:" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 36 "Op\354t si nejprve zadefinujeme funkci:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 34 "f: =x->((1+x)*(1+2*x)*(1+3*x)-1)/x:" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 48 "potom nech\341me Maple spo\350\355st p\370\355slu\232nou derivaci: " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "limit(f(x),x=0);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"'" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 65 "a nakonec si (pro lep\232\355 n\341zor a pro kontrolu) na kresl\355me obr\341zek:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 " plot(f,-2..1);" }}{PARA 13 "" 1 "" {GLPLOT2D 294 294 294 {PLOTDATA 2 " 6%-%'CURVESG6$7S7$$!\"#\"\"!$\"\")F*7$$!3&*****\\P&3Y$>!#<$\"3yLtqZscv rF07$$!3!***\\ivm y&F07$$!3#****\\P\"\\J\\:=^F07$$!3'***\\7V0@&o\"F0$\"3! \\%Het9H-XF07$$!33+]i&exdi\"F0$\"3QD*[c5j`(RF07$$!3'***\\i+#QUc\"F0$\" 37EA*GoEWZ$F07$$!3****\\i!3%f+:F0$\"3rMd'>ogT+$F07$$!3!***\\7oS:P9F0$ \"3+AWzVhx$e#F07$$!31++]<#)*=P\"F0$\"3Hk!yD#zu,AF07$$!3))***\\(G3U98F0 $\"3`?51uNe2>F07$$!31++]-\\r\\7F0$\"3P2No(4gQi\"F07$$!3!*****\\(GVZ=\" F0$\"3eXy:\"yB&*Q\"F07$$!31++](4J@7\"F0$\"3KF$ft7F;@\"F07$$!3!***\\iIK Fl5F0$\"3QYBW)zO34\"F07$$!3')*****\\FPm(**!#=$\"3wb;:lZ'p(**Ffp7$$!3() *******4'*QS*Ffp$\"3DErv:+5<'*Ffp7$$!3?++Dc>mP()Ffp$\"3sY\"p#e.w$p*Ffp 7$$!3'3+++&=$z9)Ffp$\"3LlY$4d-1-\"F07$$!3N***\\iX/4](Ffp$\"3nmC$y:>[7 \"F07$$!3C***\\(o8y%)oFfp$\"3oFU5kLvq7F07$$!33****\\i:#>C'Ffp$\"3#o9%z o8er9F07$$!3/***\\7ev:l&Ffp$\"3)p()fOD&o*p\"F07$$!3G++](o2[,&Ffp$\"3!e a1BJ4E*>F07$$!3C++D1[Q`VFfp$\"3A,BSpUR[BF07$$!3W++vVUhxPFfp$\"3#G(*\\V \\Y3q#F07$$!3O****\\iiwbJFfp$\"3l$*>Y`()=EJF07$$!30,++]kL8DFfp$\"3E:Rl 6:M9OF07$$!3)3++D@W[)=Ffp$\"3`$ot&G'H)RTF07$$!39++Dccuw7Ffp$\"3S%>qja% Q$p%F07$$!3T/++v)eb,'!#>$\"3?ar*Gp++O&F07$$\"3d#*y*****\\@8&!#@$\"3xJw LXpk0gF07$$\"3F0++]7,HlFbu$\"3cw:CI!oPu'F07$$\"3j)**\\P4w)R7Ffp$\"39kh zm75cuF07$$\"3s,++vZf\")=Ffp$\"3%)R%Qj=y@G)F07$$\"3'z**\\P/-a[#Ffp$\"3 n'fpskvX5*F07$$\"3R++v=Yb;JFfp$\"3o6C@%[)4,5!#;7$$\"3s)****\\i@Ot$Ffp$ \"3k0?QhzL%4\"Fdw7$$\"3g)**\\PfL'zVFfp$\"3+@b!y$o%o>\"Fdw7$$\"3(=+++!* >=+&Ffp$\"3K;A(GS4.I\"Fdw7$$\"3E++]i_4QcFfp$\"3d\\\"4!)=>4T\"Fdw7$$\"3 u,+vV>5piFfp$\"3h!G**)[5TD:Fdw7$$\"3U,++]:$*[oFfp$\"3j7&f2lH[j\"Fdw7$$ \"3&3++Dr\"[8vFfp$\"3uJ%RIV(>l " 0 "" {MPLTEXT 1 0 32 "f:=x->((1+x)^5-(1+5*x))/x^2+x^5:" }}}{EXCHG {PARA 0 " > " 0 "" {MPLTEXT 1 0 16 "limit(f(x),x=0);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"#5" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "plot (f, -1.5..1);" }}{PARA 13 "" 1 "" {GLPLOT2D 294 294 294 {PLOTDATA 2 "6 %-%'CURVESG6$7S7$$!3++++++++:!#<$!3++++++v=ZF*7$$!3OLLe9r]X9F*$!3`BQL7 V.RLF*7$$!3emTNYJ4)R\"F*$!33_)QI*\\7#G#F*7$$!3IL$3-=rZM\"F*$!3FaM\")4p UN7F*7$$!3QL$e9w&4\"H\"F*$!3%>\"))z\"RL)fJ!#=7$$!3nmTg_anP7F*$\"3VZ1sz UxA[FA7$$!3UL3-))z9)=\"F*$\"3:nl+#=`=8\"F*7$$!33+v=n^'o8\"F*$\"3HFZ3S \"=_s\"F*7$$!3SL3_+%GQ3\"F*$\"3s&)3mtUUmAF*7$$!3#**\\PMsh4.\"F*$\"3m&e ES21Vu#F*7$$!3ylm;z%=ew*FA$\"31!=k8r(4$=$F*7$$!3sKLeR-%oG*FA$\"3FQ1-*Q -P`$F*7$$!3Q****\\(=Cwu)FA$\"3GT*>`%H$o*QF*7$$!3h****\\iS>1#)FA$\"30UD J\"QEhB%F*7$$!3y****\\7eU%o(FA$\"3c?S&eqtja%F*7$$!3(GL3_D51@(FA$\"3P\" pvRb7#>[F*7$$!3=mm;Hx>ZmFA$\"3Mrm;f0eQ^F*7$$!3#emmmT8*phFA$\"3nQq4K5>4 aF*7$$!3z**\\(oH=Zh&FA$\"3NU`w8(H(GdF*7$$!3-nmmTlFB^FA$\"3^cuS;*[$>gF* 7$$!3M)*\\(o/(3%e%FA$\"3%R62N\"Q.]jF*7$$!3+**\\iS6lqSFA$\"3/L%*RQ0BzmF *7$$!3UkmTNY$\\`$FA$\"3_'49>@i,/(F*7$$!3Bm;/^'zH/$FA$\"3%e>MWK?#*Q(F*7 $$!3cLLeR(RB^#FA$\"39&\\/@R%R'y(F*7$$!31K$3_+a6'>FA$\"3u`^p&H>LA)F*7$$ !3i**\\7._M\"[\"FA$\"3BapF1?0D')F*7$$!3B8L$3_&QJ'*!#>$\"3#*)o&o6:M#3*F *7$$!3q(*****\\P!yF%F]t$\"3i1+4-5H\"e*F*7$$\"3kt++DcJ'f*!#?$\"3wbr-'F]t$\"3EzZbx%4@1\"F[u7$$\"3+++v$4q`;\"FA$\"3B\\H^ jy[B6F[u7$$\"3eJLLeM%4n\"FA$\"3oV$y!oT`\"=\"F[u7$$\"3=,+]P4v5AFA$\"3=! p\")p[XmC\"F[u7$$\"3_l;zWn*)*p#FA$\"3X&z8F[u7$$\"3PK$ek.Nyt$FA$\"39M%**oY#f\\9F[u7$$\"3!=+Dc^&zjU FA$\"3];AI-,WE:F[u7$$\"3EKL$3-=!yZFA$\"3:b*=`EZ`g\"F[u7$$\"3%))*\\7G8O ;`FA$\"3Y//sGvA#p\"F[u7$$\"3(*omm;*\\[$eFA$\"3QJxOB0M!y\"F[u7$$\"3%)pm T&Qz]O'FA$\"3y!zQ7T9`(=F[u7$$\"3EO$ekG=4*oFA$\"3!3%zE:Yxu>F[u7$$\"3m-+ +D'4TP(FA$\"3ki2vw:?r?F[u7$$\"3,PL3F9!z#zFA$\"31myv!>%>)=#F[u7$$\"3ipm m;%>KU)FA$\"3I,$)f\\2C*H#F[u7$$\"3g+]7. 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