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" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 54 "S funkcemi se v Maple pracuje obdobn\354 jak jsme zvykl\355." }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 23 "V\375po\350et funk\350n\355 hodnoty" }{MPLTEXT 1 0 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 6 "f(Pi);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 44 "V\375po\350et funk\350n\355 hodnoty v bod\354 kde funkce f " } {TEXT 273 15 "nen\355 definovan\341" }{TEXT -1 29 " je ukon\350en chyb ov\375m hl\341\232en\355m" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "f(0);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 9 "Spo\350teme " }{TEXT 271 6 "limi tu" }{TEXT -1 8 " funkce " }{TEXT 270 1 "f" }{TEXT -1 8 " v bod\354 " }{TEXT 269 1 "0" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "limit(f(x), x=0) ;" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 272 10 "P\370\355klad *)" }}} {EXCHG {PARA 0 "" 0 "" {TEXT -1 71 "M\371\236eme vyu\236\355t krat\232 \355ho z\341pisu a funkci zadat jen jako algebraick\375 v\375raz" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "vyraz:=x^(1/x);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 48 "Pro v\375po\350et limity pou\236ijeme op \354t funkci limit. " }}{PARA 0 "" 0 "" {TEXT 275 12 "V\232imn\354te s i:" }}{PARA 0 "" 0 "" {TEXT -1 59 " a) velk\351ho prvn\355ho p\355smen e u p\370\355kazu Limit - viz cvi\350en\355 1" }}{PARA 0 "" 0 "" {TEXT -1 40 " b) n\341sleduj\355c\355ho z\341pisu - viz cvi\350en\355 \+ 1" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 37 "Limit(vyraz, x=infinity): %=va lue(%);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 274 7 "P\370\355klad" }}} {EXCHG {PARA 0 "" 0 "" {TEXT -1 22 " Nadefinujeme si vyraz" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "g:=exp(2*(x+1))/(2*(x+1));" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 37 "Pokus\355me se spo\350\355tat limitu v bo d\354 -1" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "Limit(g, x=-1): %=value (%);" }{TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 17 "Limita neexistuje " }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 36 "Spo\350teme jednostrannou lim itu z leva" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 33 "Limit(g, x=-1, left): %=value(%);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 37 "Spo\350teme jedno strannou limitu z prava" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 34 "Limit(g, x=-1, right): %=value(%);" }}}{SECT 0 {PARA 4 "" 0 "" {TEXT -1 19 " \332lohy k vypracov\341n\355" }}{EXCHG {PARA 15 "" 0 "" {TEXT -1 80 "U ve\357te libovolnou funkci jej\355\236 limita v bod\354 2 je nekone \350no. Dokladujte v\375po\350tem" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}} {EXCHG {PARA 15 "" 0 "" {TEXT -1 32 "Vypo\350t\354te limitu slo\236en \351 funkce " }{TEXT 279 1 "f" }{TEXT -1 8 " v bod\354 " }{XPPEDIT 257 0 "x=0" "6#/%\"xG\"\"!" }{TEXT -1 7 ", kde " }{XPPEDIT 261 0 "f(x ) = 2*x^3-3*x-10" "6#/-%\"fG6#%\"xG,(*&\"\"#\"\"\"*$F'\"\"$F+F+*&F-F+F 'F+!\"\"\"#5F/" }{TEXT -1 5 " pro " }{XPPEDIT 259 0 "x>2" "6#2\"\"#%\" xG" }{TEXT -1 3 " a " }{XPPEDIT 260 0 "f(x) = abs(x-2)" "6#/-%\"fG6#% \"xG-%$absG6#,&F'\"\"\"\"\"#!\"\"" }{TEXT -1 5 " pro " }{XPPEDIT 258 0 "x<2" "6#2%\"xG\"\"#" }}{PARA 257 "" 0 "" {TEXT 278 6 "N\341vod:" } {TEXT -1 42 " k defnici slo\236en\351 funkce pou\236ijte p\370\355kaz \+ " }{HYPERLNK 17 "piecewise" 2 "piecewise" "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}} }{SECT 0 {PARA 4 "" 0 "" {TEXT -1 27 " M\355sto pro Va\232e experiment y" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 " " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}}{SECT 1 {PARA 4 " " 0 "" {TEXT 276 22 " Roz\232\355\370en\355 - knihovna " }{HYPERLNK 17 "Student" 2 "Student" "" }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 62 "Knih ovna (nebo t\351\236 bal\355k z anglick\351ho p\370ekladu slova packag e) " }{HYPERLNK 17 "Student" 2 "Student" "" }{TEXT -1 115 " je zam\354 \370ena na v\375uku matematiky, kde d\371raz je kladen na vizualizaci \+ a krokov\375 pr\371b\354h v\375po\350tu - metoda Step-by-Step" }} {PARA 0 "" 0 "" {TEXT -1 89 "Obsahov\354 je rozd\354lena do p\354ti te matick\375ch celk\371. N\341s budou p\370edev\232\355m zaj\355mat podk nihovny " }{HYPERLNK 17 "Precalculus" 2 "Precalculus" "" }{TEXT -1 3 " a " }{HYPERLNK 17 "Calculus1" 2 "Calculus1" "" }{MPLTEXT 1 0 0 "" }}} {EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 27 "Knihovny na\350\355t\341me p\370\355kazem " }{HYPERLNK 17 "with " 2 "with" "" }{TEXT -1 3 ". \n" }{TEXT 277 6 "Pozor!" }{TEXT -1 109 " Ve\232ker\351 podknihovny se mus\355 na\350\355st zvl\341\232\235. Po uh\375m na\350ten\355m cel\351 knihovny Student se podknihovny nezp \370\355stupn\355" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "with(Student[C alculus1]);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 82 "Vra\235me se zp\354t k p\370\355kladu *) kde js me z\355skali p\370\355m\375m v\375po\350etem okam\236it\354 v\375sled ek. " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "Limit(x^(1/x), x=in finity);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "Hint(%);" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "Rule[%](%%);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "Hint(%);" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 12 "Rule[%](%%);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "Hint(%);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "Rule[%]( %%);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "Hint(%);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "Rule[%](%%);" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 8 "Hint(%);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "Rule[%](%%);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 64 "Pro tyto \+ \372\350ely je sou\350ast\355 knihovny Student[Calculus1] i Maplet " } {HYPERLNK 17 "LimitTutor" 2 "LimitTutor" "" }{TEXT -1 1 "." }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 32 "LimitTutor(x^(1/x), x=infinity);" }}} {EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 111 "V n\354kter\375ch p\370\355padech je v\232ak postup v\375po \350tu v porovn\341n\355 s ru\350n\355m po\350\355t\341n\355m zna\350n \354 zdlouhav\375 a t\355m nep\370ehledn\375." }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 43 "LimitTutor((1-cos(x^2))/x^2/sin(x^2), x=0);" }}}}} {SECT 1 {PARA 4 "" 0 "" {TEXT -1 1 " " }{TEXT 290 7 "P\370\355kaz " } {HYPERLNK 17 "plot" 2 "plot" "" }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 84 " V t\351to \350\341sti si uk\341\236eme mo\236nosti, kter\351 Maple nab \355z\355 p\370i pr\341ci s grafick\375m v\375stupem." }}{PARA 0 "" 0 "" {TEXT -1 30 "P\370edvedeme si z\341kladn\355 p\370\355kaz " } {HYPERLNK 17 "plot" 2 "plot" "" }{TEXT -1 42 " pro tvorbu graf\371 a v dal\232\355 \350\341sti p\370\355kazy " }{HYPERLNK 17 "animate" 2 "pl ots[animate]" "" }{TEXT -1 3 " a " }{HYPERLNK 17 "display" 2 "plots[di splay] " "" }{TEXT -1 53 " pro pr\341ci s animacemi, kter\351 jsou sou \350\341st\355 knihovny " }{HYPERLNK 17 "plots" 2 "plots" "" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "f:=sin(x);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 38 "Vykresl\355me graf funkce f na intervalu " } {XPPEDIT 18 0 "-Pi..Pi" "6#;,$%#PiG!\"\"F%" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "plot(f, x=-Pi..Pi);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 64 "Rozsah zobrazen\375ch funk\350n\355ch hodnot lze omezit interva lem hodnot" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "plot(x^(-2), x=-3..3, 0..10);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 64 "V\355ce graf\371 zobr az\355me p\370\355kazem plot pokud zad\341me seznam (mno\236inu)" }} {PARA 0 "> " 0 "" {MPLTEXT 1 0 34 "plot([sin(x), cos(x)], x=-Pi..Pi); " }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 75 "Nastav\355me pom\354r os x a \+ y v pom\354ru 1:1. Barvu graf\371 lze nastavit parametrem " } {HYPERLNK 17 "color" 2 "plot[color]" "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 76 "plot([sin(x), cos(x)], x=-Pi..Pi, scaling=constrained, color=[ blue, black]);" }}}{SECT 0 {PARA 4 "" 0 "" {TEXT -1 19 "\332lohy k vyp racov\341n\355" }}{EXCHG {PARA 15 "" 0 "" {TEXT -1 23 "Nakreslete graf funkce " }{XPPEDIT 18 0 "exp(sin(x))" "6#-%$expG6#-%$sinG6#%\"xG" } {TEXT -1 52 " a jej\355 prvn\355 derivace do jednoho obr\341zku.\nPou \236ijte " }{TEXT 294 28 "3 dosud neuveden\351 vlastnosti" }{TEXT -1 24 " (nastaven\355) pro funkci " }{TEXT 293 4 "plot" }{TEXT -1 1 "\n" }{TEXT 292 6 "N\341vod:" }{TEXT -1 38 " n\341pov\354du pro volby nasta ven\355 p\370\355kazu " }{TEXT 291 4 "plot" }{TEXT -1 15 " naleznete z de " }{HYPERLNK 17 "plot[options]" 2 "plot[options]" "" }{TEXT -1 31 " nebo interaktivn\355ho pomocn\355ka " }{HYPERLNK 17 "interactive" 2 " plots[interactive]" "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "in teractive(exp(sin(x)));" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 " " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{SECT 0 {PARA 4 " " 0 "" {TEXT -1 27 " M\355sto pro Va\232e experimenty" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 1 " " }{TEXT 281 6 "P\370\355kaz" }{TEXT 295 1 " " }{HYPERLNK 17 "displa y" 2 "plots[display]" "" }{TEXT 282 1 " " }{TEXT 296 1 "a" }{TEXT 297 1 " " }{HYPERLNK 17 "animate" 2 "plots[animate]" "" }}{EXCHG {PARA 0 " " 0 "" {TEXT -1 104 "Pro slo\236it\354j\232\355 konstrukce je pou\236i t\355 samotn\351ho p\370\355kazu plot nedostate\350n\351. \nOv\232em v kombinaci s p\370\355kazem " }{HYPERLNK 17 "display" 2 "plots[display ]" "" }{TEXT -1 33 " lze doc\355lit kvalitn\355ch v\375sledk\371." }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "with(plots);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 56 "Grafy, kter\351 bude cht\355t zobrazit p \370i\370ad\355me do prom\354nn\375ch" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 63 "p1:=plot(x^2, x=-5..5, style=point, color=blue, symbolsize=20): " }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "p2:=plot(x^2, x=-5..5):" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "display([p1,p2]);" }}} {EXCHG {PARA 259 "" 0 "" {TEXT -1 8 "P\370\355klad " }{TEXT 288 3 "**) " }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 38 "Vytvo\370\355me si posloupnos t graf\371 funkce " }{XPPEDIT 18 0 "sin(i*x)" "6#-%$sinG6#*&%\"iG\"\" \"%\"xGF(" }{TEXT -1 6 ", kde " }{XPPEDIT 18 0 "i = 1..10" "6#/%\"iG; \"\"\"\"#5" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 63 "posloupnost_grafu:=se q(plot(sin(i*x), x=-2*Pi..2*Pi), i=1..10):" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 34 "Pro p\370\355pad animace dopln\355me volbu " }{TEXT 286 15 "insequence=true" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 67 "display([pos loupnost_grafu], scaling=constrained, insequence=true);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 7 "P\370\355kaz " }{HYPERLNK 17 "animate" 2 " plots[animate]" "" }{TEXT -1 35 " pro vytv\341\370en\355 jednodu\232 \232\355ch animac\355" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 87 "animate( p lot, [[cos(t), sin(t), t=0..A]], A=0..2*Pi, scaling=constrained, frame s=50);\n" }}}{SECT 0 {PARA 4 "" 0 "" {TEXT -1 19 "\332lohy k vypracov \341n\355" }}{EXCHG {PARA 15 "" 0 "" {TEXT -1 24 "Dopl\362te \370e\232 en\355 p\370\355kladu " }{TEXT 287 3 "**)" }{TEXT -1 24 " o textov\375 popis grafu \n" }{TEXT 289 6 "N\341vod:" }{TEXT -1 18 " pou\236ijte \+ p\370\355kaz " }{HYPERLNK 17 "textplot" 2 "plots[textplot]" "" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 15 "" 0 "" {TEXT -1 37 "Vytvo\370t e animaci pulsuj\355c\355 kardioidy\n" }{TEXT 283 6 "N\341vod:" } {TEXT -1 47 " rovnice kardioidy v pol\341rn\355ch sou\370adnic\355ch j e " }{XPPEDIT 18 0 "A*(1-sin(t))" "6#*&%\"AG\"\"\",&F%F%-%$sinG6#%\"tG !\"\"F%" }{TEXT -1 6 ", kde " }{TEXT 284 1 "t" }{TEXT -1 11 " je \372h el a " }{TEXT 285 1 "A" }{TEXT -1 25 " ud\341v\341 velikost kardioidy " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 0 "" }}}}{SECT 0 {PARA 4 "" 0 "" {TEXT -1 27 " M \355sto pro Va\232e experimenty" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{PARA 5 "" 0 "" {TEXT -1 0 "" }}}{PARA 0 "" 0 " " {TEXT -1 0 "" }}}{MARK "3 0 7" 7 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 } {PAGENUMBERS 0 1 2 33 1 1 }