{VERSION 2 3 "IBM INTEL NT" "2.3" } {USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 0 1 255 0 0 1 0 1 0 0 1 0 0 0 0 }{CSTYLE "2D Math" -1 2 "Times" 0 1 0 0 0 0 0 0 2 0 0 0 0 0 0 }{CSTYLE "2D Comment" 2 18 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 } {CSTYLE "2D Input" 2 19 "" 0 1 255 0 0 1 0 0 0 0 0 0 0 0 0 }{CSTYLE "2 D Output" 2 20 "" 0 1 0 0 255 1 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 256 " " 0 1 49 48 48 0 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 257 "" 0 1 176 0 15 0 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 258 "" 0 1 0 0 105 0 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 259 "" 0 1 0 0 120 0 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 260 "" 0 1 0 0 105 0 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 261 "" 0 1 0 0 192 0 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 262 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 263 "" 0 1 109 101 115 0 0 1 0 0 0 0 0 0 0 } {CSTYLE "" -1 264 "" 0 1 32 106 97 0 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 265 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 266 "" 0 1 101 108 112 0 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 267 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 268 "" 0 1 32 79 112 0 0 1 0 0 0 0 0 0 0 } {CSTYLE "" -1 269 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 270 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 271 "" 0 1 0 0 224 0 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 272 "" 0 1 116 101 99 0 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 273 "" 0 1 0 0 113 0 0 1 0 0 0 0 0 0 0 }{CSTYLE " " -1 274 "" 0 1 0 0 65 0 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 275 "" 0 1 101 32 105 0 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 276 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 277 "" 0 1 32 79 112 0 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 278 "" 0 1 24 0 0 0 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 279 "" 0 1 0 0 65 0 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 280 "" 0 1 0 0 101 0 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 281 "" 0 1 0 0 16 0 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 286 "" 0 1 141 0 0 0 0 1 0 0 0 0 0 0 0 } {CSTYLE "" -1 287 "" 0 1 245 101 115 0 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 288 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 289 "" 0 1 0 0 128 0 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 290 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 291 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 292 "" 0 1 80 1 3 0 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 293 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 294 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 295 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 296 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 299 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 }{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 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "Text Output" -1 2 1 {CSTYLE "" -1 -1 "Courier" 1 10 0 0 255 1 0 0 0 0 0 1 3 0 0 }1 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "Warning" 2 7 1 {CSTYLE "" -1 -1 "" 0 1 0 0 255 1 0 0 0 0 0 0 1 0 0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "Error" 7 8 1 {CSTYLE "" -1 -1 "" 0 1 255 0 255 1 0 0 0 0 0 0 0 0 0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "Map le Output" 0 11 1 {CSTYLE "" -1 -1 "" 0 1 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 }1 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 } {PSTYLE "Maple Plot" 0 13 1 {CSTYLE "" -1 -1 "" 0 1 189 0 32 0 0 0 0 0 0 0 0 0 0 }3 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 0 256 1 {CSTYLE "" -1 -1 "" 0 1 0 0 105 0 0 0 0 0 0 0 0 0 0 }3 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 0 257 1 {CSTYLE "" -1 -1 "" 0 1 59 1 103 0 0 0 0 0 0 0 0 0 0 }3 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 0 258 1 {CSTYLE "" -1 -1 "" 0 1 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 {EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 258 "" 0 "" {TEXT 256 6 "AULA 4" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 " " {TEXT -1 26 "Nesta aula aprenderemos a:" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 23 "- descrever intervalos;" }}{PARA 0 "" 0 "" {TEXT -1 17 "- usar o comando " }{TEXT 257 25 "solve(express \343o,vari\341vel)" }{TEXT -1 26 " para resolver inequa\347\365es;" }} {PARA 0 "" 0 "" {TEXT -1 114 "- escrever express\365es que signifiquem fun\347\365es e trabalhar com composi\347\343o e avalia\347\343o de f un\347\365es em valores dados.;" }}{PARA 0 "" 0 "" {TEXT -1 46 "- util izar a biblioteca de fun\347\365es do Maple V." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 259 10 "Intervalos" }}{PARA 0 " " 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 171 "Na descri\347\343 o de intervalos devemos estar atentos a algumas express\365es que usua lmente usamos em matem\341tica, mas que o pacote matem\341tico do Map le V n\343o \351 capaz de entender." }}{PARA 0 "" 0 "" {TEXT -1 35 "Po r exemplo, pensemos no intervalo " }{XPPEDIT 18 0 "[-infinito,3]" "7$, $%)infinitoG!\"\"\"\"$" }{TEXT -1 83 ", que significa todos os n\372m eros reais menores que 3. Como grafar isso no Maple V?" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "x<=3;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#1%\"xG\"\"$" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 84 "Observe o qu e ocorre quando queremos escrevemos o sinal igual antes da desigualdad e:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "x=<3;" }}{PARA 8 "" 1 "" {TEXT -1 28 "Syntax error, `;` unexpected" }}}{EXCHG {PARA 0 "" 0 " " {TEXT 286 62 "\351 importante que grafemos sempre a desigualdade ant es do igual" }{TEXT -1 94 ". Agora observe o que ocorre quando queremo s grafar o intervalo de n\372meros reais entre -3 e 5." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "-3<=x<=5;" }}{PARA 8 "" 1 "" {TEXT -1 44 "Syntax error, unexpected relational operator" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 36 "Para grafar intervalos deste tipo \351 " } {TEXT 287 40 "necess\341rio que utilizemos dos conectivos" }{TEXT -1 9 " l\363gicos " }{TEXT 258 4 "and " }{TEXT -1 1 "e" }{TEXT 260 5 " or . " }{TEXT -1 12 "Por exemplo," }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "3<=x and x<=5;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#31,&\"\"$\" \"\"%\"xG!\"\"\"\"!1,&F(F'!\"&F'F*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "x<=-3 or x>=5;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#51, &%\"xG\"\"\"\"\"$F'\"\"!1,&\"\"&F'F&!\"\"F)" }}}{EXCHG {PARA 0 "" 0 " " {TEXT -1 20 "Do mesmo modo que o " }{TEXT 261 16 "solve(exp.,var.)" }{TEXT -1 128 " \351 utilizado para resolver equa\347\365es (achando a s suas ra\355zes) ele tamb\351m pode ser usado para resolver desiguald ades. Por exemplo:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "solve (x-3>=5,x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%*RealRangeG6$\"\")%)i nfinityG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "solve(x^2-1>=-1 ,x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%\"xG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "solve(x^2-1>=0,x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$-%*RealRangeG6$,$%)infinityG!\"\"F(-F$6$\"\"\"F'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "solve(x^2-1>=0 and x^2-1<2,x);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6$-%*RealRangeG6$-%%OpenG6#,$*$\"\"$#\" \"\"\"\"#!\"\"F/-F$6$F--F'6#F*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "solve(x^2-1<-2,x);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 262 178 "O bserve que no caso de n\343o haver solu\347\343o, ou seja, o conjunto \+ solu\347\343o ser o conjunto vazio, nada \351 produzido pelo Maple V. \+ Portanto, cuidado com a leitura das respostas obtidas." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 263 7 "Fun\347\365es" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }} {PARA 0 "" 0 "" {TEXT 280 42 "Calculando o valor de uma fun\347\343o n um ponto" }{TEXT -1 1 "." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 " " 0 "" {TEXT -1 85 "O Maple V possui uma serie de fun\347\365es previa mente definidas, faremos uma consulta ao " }{TEXT 264 4 "Help" }{TEXT -1 145 " do Maple V para saber como proceder com a fun\347\343o logari tmo (os procedimentos utilizados s\343o id\352nticos para a procura de outra fun\347\343o qualquer )." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }} {PARA 0 "" 0 "" {TEXT 281 9 "Exerc\355cio" }{TEXT -1 54 ": tente fazer o mesmo para as fun\347\365es trigonom\351tricas!" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 41 "Procurando a fun\347\343o logaritmo: clique em " }{TEXT 265 19 "Help, Topic Search " }{TEXT -1 143 "e a\355 escreva \"l\" (a letra L min\372scula). O que aconteceu? \+ Procure ent\343o nessa janela se voc\352 encontra algo parecido com lo garitmo? E agora Jos\351?" }}{PARA 0 "" 0 "" {TEXT -1 9 "Volte ao " } {TEXT 266 34 "Help, Contents, Index e Function. " }}{PARA 0 "" 0 "" {TEXT -1 100 "Procure ent\343o por express\365es como log, ln e log10. Leiam ent\343o seu significado e voltemos ao prompt." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 74 "Observe que n\343o som ente o Maple V entende do logaritmo neperiano (na base " }{TEXT 267 1 "e" }{TEXT -1 118 "), como tamb\351m na base 10, e qualquer que seja a base. Tentemos ent\343o calcular alguns valores para a fun\347\343o l ogaritmo." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "log(10);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#-%#lnG6#\"#5" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "evalf(\");" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\" +$4&e-B!\"*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 6 "ln(e);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#-%#lnG6#%\"eG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "evalf(\");" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%# lnG6#%\"eG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "log[10](10); " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"\"" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 6 "log10;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%&log10G" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "log10(10);" }}{PARA 11 " " 1 "" {XPPMATH 20 "6#\"\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "log(10);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%#lnG6#\"#5" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "evalf(\");" }}{PARA 11 "" 1 " " {XPPMATH 20 "6#$\"+$4&e-B!\"*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "log[2](8);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*&-%#lnG6#\"\") \"\"\"-F%6#\"\"#!\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {XPPEDIT 19 1 "eval f(\");" "-%&evalfG6#%\"\"G" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+++++ I!\"*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 6 "ln(1);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"!" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 7 "log(1);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"!" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "log1;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%%log1G" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "evalf(\"); " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%%log1G" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 6 "log10;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%&log10G " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "evalf(\");" }}{PARA 11 " " 1 "" {XPPMATH 20 "6#%&log10G" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "log(10);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%#lnG6#\"#5" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "evalf(\");" }}{PARA 11 "" 1 " " {XPPMATH 20 "6#$\"+$4&e-B!\"*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "log10(10);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"\"" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "ln(exp(1));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "log(exp(1));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "log10(exp(1));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*$-%#lnG6#\"#5!\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "evalf(\");" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+>[%H M%!#5" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 6 "ln(0);" }}{PARA 8 " " 1 "" {TEXT -1 38 "Error, (in ln) singularity encountered" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 60 "Observe que o Maple V reconhece as singul aridades da fun\347\343o!" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 7 "ln(-1);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*&%\"IG\"\"\"%#PiGF%" }}} {EXCHG {PARA 0 "" 0 "" {TEXT -1 98 "Para valores negativos ele trabalh a com a defini\347\343o do logaritmo como fun\347\343o de vari\341vel \+ complexa." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "ln(1+I);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#-%#lnG6#,&\"\"\"F'%\"IGF'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "evalf(\");" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,&$\"+.ftlM!#5\"\"\"%\"IG$\"+M;)R&yF&" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "tan(Pi/2);" }}{PARA 8 "" 1 "" {TEXT -1 39 "Error, (in tan) singularity encountered" }}}{EXCHG {PARA 0 "" 0 " " {TEXT -1 69 "Novamente o Maple V reconheceu os valores de singularid ade da fun\347\343o." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "x:=3;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#> %\"xG\"\"$" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "f:=ln(x);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"fG-%#lnG6#\"\"$" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "evalf(\");" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+*G7')4\"!\"*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "s ubs(x=3,f);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%#lnG6#\"\"$" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 6 "ln(3);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%#lnG6#\"\"$" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "evalf(\");" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+*G7')4\"!\"*" } }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "f:=sin(y);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"fG-%$sinG6#%\"yG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "y:=Pi/2;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"yG,$%# PiG#\"\"\"\"\"#" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "f(y);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 7 "y:=z+2;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"yG,&%\" zG\"\"\"\"\"#F'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "f(y);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#--%$sinG6#,&%\"zG\"\"\"\"\"#F)F&" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "g:=cos(y);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"gG-%$cosG6#,&%\"zG\"\"\"\"\"#F*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "f(g);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#--%$sinG6#,&%\"zG\"\"\"\"\"#F)6#-%$cosGF&" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 22 "Observe que o Maple V " }{TEXT 288 51 "n\343o est \341 reconhecendo o que \351 composi\347\343o de fun\347\365es" } {TEXT -1 53 ". Como isso pode ser feito???????????????????????????" }} {PARA 0 "" 0 "" {TEXT -1 37 "Uma maneira \351 utilizarmos o operador \+ " }{TEXT 290 2 "@." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "f:=sin(x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"fG-%$sinG6#%\"xG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 " g:=cos(x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"gG-%$cosG6#%\"xG" }} }{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "h:=f@g(x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"hG-%\"@G6$-%$sinG6#%\"xG--%$cosGF*F*" }}} {EXCHG {PARA 0 "" 0 "" {TEXT -1 78 "Observe que ele continua n\343.o e ntendendo! Utilizemos ent\343o as fun\347\365es somente:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "h:=(sin@cos)(x);" }}{PARA 11 "" 1 " " {XPPMATH 20 "6#>%\"hG-%$sinG6#-%$cosG6#%\"xG" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 22 "Uma outra forma seria " }{TEXT 295 37 " realizar a s ubstitui\347\343o diretamente " }{TEXT -1 2 "ou" }{TEXT 299 1 " " } {TEXT -1 15 "usar o comando " }{TEXT 296 5 "subs:" }}}{EXCHG {PARA 0 " > " 0 "" {MPLTEXT 1 0 10 "x:=cos(z);" }}{PARA 11 "" 1 "" {XPPMATH 20 " 6#>%\"xG-%$cosG6#%\"zG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "f :=sin(x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"fG-%$sinG6#-%$cosG6#% \"zG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "h:=subs(x=cos(z),si n(x));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"hG-%$sinG6#-%$cosG6#%\"z G" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "subs(z=Pi/2,f);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#-%$sinG6#-%$cosG6#,$%#PiG#\"\"\"\"\"# " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "evalf(\");" }}{PARA 11 " " 1 "" {XPPMATH 20 "6#\"\"!" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "subs(z=Pi/2,h);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%$sinG6#-%$cos G6#,$%#PiG#\"\"\"\"\"#" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "ev alf(\");" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"!" }}}{EXCHG {PARA 0 " " 0 "" {TEXT 292 42 "Como escrever fun\347\365es definidas por partes " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 29 " Aces se pelo Help o comando " }{TEXT 291 10 "piecewise " }{TEXT -1 9 "(ent re em" }{TEXT 293 21 " Help, Topic Search, " }{TEXT -1 21 " e localize piecewise" }{TEXT 294 2 ")." }}{PARA 0 "" 0 "" {TEXT -1 162 "Observem os ent\343o os exemplos. Suponha que voc\352 quer definir uma fun\347 \343o que para valores menores ou iguais que 0 vale x+2 e para valores maiores que 0 vale sen(x)." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 35 "p:= piecewise(t<=0,t+2,t>0,s in(t));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"pG-%*PIECEWISEG6$7$,&% \"tG\"\"\"\"\"#F+1F*\"\"!7$-%$sinG6#F*2F.F*" }}}{EXCHG {PARA 0 "" 0 " " {TEXT -1 64 "Veja o que acontece se voc\352 utilizar a vari\341vel x no lugar de t?" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 35 "p:= piec ewise(x<=0,x+2,x>0,sin(x));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"pG- %$sinG6#\"\"$" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 53 "Pe\347a agora ao Maple o valor de x que ele est\341 usando!" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 2 "x;" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"$" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 122 "Definamos agora uma fun\347\343o que vale seno para valores de x \+ maiores que 3, 1 em x igual a 3 e 0 para valores menores que 3." }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 40 "g:= piecewise(x<3,0,x=3,1,x> 3,sin(x));\n\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"gG-%*PIECEWISEG6 %7$\"\"!2%\"xG\"\"$7$\"\"\"/F+F,7$-%$sinG6#F+2F,F+" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }} {PARA 0 "" 0 "" {TEXT 268 11 "Bibliotecas" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 14 "As bibliotecas" }{TEXT 277 1 " " } {TEXT -1 132 "s\343o pacotes de procedimentos dentro do Maple V utiliz ados para resolver problemas. Para acessar tais pacotes, ou como s\343 o chamados, " }{TEXT 275 10 "libraries " }{TEXT -1 33 "(em ingl\352s), utilizamos o comando" }{TEXT 270 1 " " }}{PARA 0 "" 0 "" {TEXT -1 0 " " }}{PARA 256 "" 0 "" {TEXT 276 25 "with(nome_da_biblioteca):" }} {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 49 "Para conh ecer as bibliotecas dispon\355veis acesse: " }{TEXT 269 47 "Help, Cont ents, System, Libraries and Packages," }{TEXT -1 66 " teremos ent\343o uma lista da bibliotecas dispon\355veis. Acesse ent\343o " }{TEXT 271 8 "packages" }{TEXT -1 68 ", ir\341 ent\343o aparecer uma lista de pacotes dispon\355veis. Acesse ent\343o " }{TEXT 272 7 "student" } {TEXT -1 255 ", dentro deste pacote voc\352 encontra instru\347\365es \+ de quais procedimentos devem ser realizados com esse pacote e como uti liz\341-lo (o mesmo ocorre com cada uma das possibilidades, explore um pouco esses pacotes). Prosseguiremos agora trabalhando um pouco com o " }{TEXT 289 7 "student" }{TEXT -1 2 ". " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 278 17 "O pacote student:" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 20 "O pacote denominado \+ " }{TEXT 274 8 "student " }{TEXT -1 160 "\351 uma cole\347\343o de rot inas destinadas \340 solu\347\365es de problemas que necessitam ser ex ecutados passo a passo, como por exemplo, resolver integrais ou deriva r fun\347\365es" }{TEXT 279 1 "," }{TEXT -1 39 " o qual pode ser acess ado pelo comando " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 257 "" 0 " " {TEXT 273 14 "with(student):" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "with(student);" }}{PARA 12 " " 1 "" {XPPMATH 20 "6#7E%\"DG%%DiffG%*DoubleintG%$IntG%&LimitG%(Linein tG%(ProductG%$SumG%*TripleintG%*changevarG%(combineG%/completesquareG% )distanceG%'equateG%(extremaG%*integrandG%*interceptG%)intpartsG%(isol ateG%(leftboxG%(leftsumG%)makeprocG%)maximizeG%*middleboxG%*middlesumG %)midpointG%)minimizeG%(powsubsG%)rightboxG%)rightsumG%,showtangentG%( simpsonG%&slopeG%*trapezoidG%&valueG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "leftbox(x^2,x=0..5,10);" }}{PARA 13 "" 1 "" {INLPLOT "6/-%'CURVESG6&7S7$\"\"!F(7$$\"1LLL3x&)*3\"!#;$\"1&e8W#)*y(=\"!#<7$$\" 1nm\"H2P\"Q?F,$\"1=t*zs-S:%F/7$$\"1LL$eRwX5$F,$\"1!\\lvf%RQ'*F/7$$\"1M L$3x%3yTF,$\"1VpAN#Rcu\"F,7$$\"1nm\"z%4\\Y_F,$\"1_rlEnc_FF,7$$\"1MLeR- /PiF,$\"1t\"=]4n+*QF,7$$\"1***\\il'pisF,$\"1#\\q?FwYF&F,7$$\"1MLe*)>VB $)F,$\"1=>_3?&z#pF,7$$\"1++DJbw!Q*F,$\"16)G_>w)*z)F,7$$\"1nm;/j$o/\"!# :$\"1E8sZi'e4\"Fen7$$\"1LL3_>jU6Fen$\"1p<#zx2cI\"Fen7$$\"1++]i^Z]7Fen$ \"1-%H?8)oj:Fen7$$\"1++](=h(e8Fen$\"15klk>BY=Fen7$$\"1++]P[6j9Fen$\"1^ ErF]qS@Fen7$$\"1L$e*[z(yb\"Fen$\"1C1&Qq$)pU#Fen7$$\"1nm;a/cq;Fen$\"1Sb -JAx!z#Fen7$$\"1nmm;t,mFen$\"1yc*3l')>!RFen7$$\"1+]i!f#=$3#Fen$\"1)3$) eq\\'RVFen7$$\"1+](=xpe=#Fen$\"1moffm-yZFen7$$\"1nm\"H28IH#Fen$\"1Onc_ *3zD&Fen7$$\"1n;zpSS\"R#Fen$\"1Zh,DM\")=dFen7$$\"1LL3_?`(\\#Fen$\"1'e$ =^jmPiFen7$$\"1M$e*)>pxg#Fen$\"1*yN]>g/!oFen7$$\"1+]Pf4t.FFen$\"1eGo+6 ;5tFen7$$\"1MLe*Gst!GFen$\"1p.Ks\"R8)yFen7$$\"1+++DRW9HFen$\"11%p>R$)R \\)Fen7$$\"1++DJE>>IFen$\"1+VfWT_:\"*Fen7$$\"1+]i!RU07$Fen$\"1\"f(o6[y P(*Fen7$$\"1++v=S2LKFen$\"1G;2hnFX5!#97$$\"1mmm\"p)=MLFen$\"1)yjJU\"o6 6Fau7$$\"1++](=]@W$Fen$\"1H1L\"zR[=\"Fau7$$\"1L$e*[$z*RNFen$\"1Y^5z`9` 7Fau7$$\"1,+]iC$pk$Fen$\"1KOgQ;,I8Fau7$$\"1m;H2qcZPFen$\"1-TTZeU/9Fau7 $$\"1+]7.\"fF&QFen$\"1c7nq_P%[\"Fau7$$\"1mm;/OgbRFen$\"1K'Ht)*zYc\"Fau 7$$\"1+]ilAFjSFen$\"1K(f/:=5l\"Fau7$$\"1MLL$)*pp;%Fen$\"1,,?%)QOOFau7$ $\"1,++D>#[Z%Fen$\"1rg/EJS-?Fau7$$\"1nmT&G!e&e%Fen$\"1+-SbYv-@Fau7$$\" 1MLL$)Qk%o%Fen$\"1U_OJ))e%>#Fau7$$\"1+]iSjE!z%Fen$\"1$[79;lYH#Fau7$$\" 1,]P40O\"*[Fen$\"1FtEj2a#R#Fau7$$\"\"&F($\"#DF(-%'COLOURG6&%$RGBG$\"*+ +++\"!\")F(F(-%*THICKNESSG6#\"\"#-%&STYLEG6#%%LINEG-%)POLYGONSG6$7&F'F '7$$\"+++++]!#5F(Fj[l-%&COLORG6&Fjz$\"\"(!\"\"$\"\"*Fc\\lFa\\l-Fg[l6$7 &Fj[l7$F[\\l$\"+++++DF]\\l7$$\"\"\"F(Fj\\l7$F]]lF(F^\\l-Fg[l6$7&F_]l7$ F]]lF]]l7$$\"+++++:!\"*F]]l7$Fe]lF(F^\\l-Fg[l6$7&Fh]l7$Fe]l$\"++++]AFg ]l7$$Fa[lF(F]^l7$F`^lF(F^\\l-Fg[l6$7&Fa^l7$F`^l$\"\"%F(7$$F[]lFg]lFf^l 7$Fi^lF(F^\\l-Fg[l6$7&Fj^l7$Fi^l$\"++++]iFg]l7$$\"\"$F(F__l7$Fb_lF(F^ \\l-Fg[l6$7&Fd_l7$Fb_l$Fe\\lF(7$$\"+++++NFg]lFi_l7$F[`lF(F^\\l-Fg[l6$7 &F]`l7$F[`l$\"++++D7F][l7$Ff^lFb`l7$Ff^lF(F^\\l-Fg[l6$7&Fe`l7$Ff^l$\"# ;F(7$$\"+++++XFg]lFj`l7$F]alF(F^\\l-Fg[l6$7&F_al7$F]al$\"++++D?F][l7$F czFdal7$FczF(F^\\l-%+AXESLABELSG6$%\"xG%!G-%%VIEWG6$;F(Fcz%(DEFAULTG" 2 250 250 250 2 0 1 0 2 9 0 4 2 1.000000 45.000000 45.000000 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 216 22651 0 0 0 0 0 1 }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "rightbox(x^2,x=0..5,10);" }}{PARA 13 "" 1 "" {INLPLOT "6/-%)POLYGONSG6$7&7$\"\"!F(7$F($\"+++++D!#57$$\"+ ++++]F,F*7$F.F(-%&COLORG6&%$RGBG$\"\"(!\"\"$\"\"*F7F5-F$6$7&F07$F.$\" \"\"F(7$F>F>7$F>F(F1-F$6$7&FA7$F>$\"++++]A!\"*7$$\"+++++:FHFF7$FJF(F1- F$6$7&FL7$FJ$\"\"%F(7$$\"\"#F(FQ7$FTF(F1-F$6$7&FV7$FT$\"++++]iFH7$$F+F HFen7$FhnF(F1-F$6$7&Fin7$Fhn$F9F(7$$\"\"$F(F^o7$F`oF(F1-F$6$7&Fbo7$F`o $\"++++D7!\")7$$\"+++++NFHFgo7$F[pF(F1-F$6$7&F]p7$F[p$\"#;F(7$FQFbp7$F QF(F1-F$6$7&Fep7$FQ$\"++++D?Fio7$$\"+++++XFHFjp7$F]qF(F1-F$6$7&F_q7$F] q$\"#DF(7$$\"\"&F(Fdq7$FgqF(F1-%'CURVESG6&7SF'7$$\"1LLL3x&)*3\"!#;$\"1 &e8W#)*y(=\"!#<7$$\"1nm\"H2P\"Q?Far$\"1=t*zs-S:%Fdr7$$\"1LL$eRwX5$Far$ \"1!\\lvf%RQ'*Fdr7$$\"1ML$3x%3yTFar$\"1VpAN#Rcu\"Far7$$\"1nm\"z%4\\Y_F ar$\"1_rlEnc_FFar7$$\"1MLeR-/PiFar$\"1t\"=]4n+*QFar7$$\"1***\\il'pisFa r$\"1#\\q?FwYF&Far7$$\"1MLe*)>VB$)Far$\"1=>_3?&z#pFar7$$\"1++DJbw!Q*Fa r$\"16)G_>w)*z)Far7$$\"1nm;/j$o/\"!#:$\"1E8sZi'e4\"F`u7$$\"1LL3_>jU6F` u$\"1p<#zx2cI\"F`u7$$\"1++]i^Z]7F`u$\"1-%H?8)oj:F`u7$$\"1++](=h(e8F`u$ \"15klk>BY=F`u7$$\"1++]P[6j9F`u$\"1^ErF]qS@F`u7$$\"1L$e*[z(yb\"F`u$\"1 C1&Qq$)pU#F`u7$$\"1nm;a/cq;F`u$\"1Sb-JAx!z#F`u7$$\"1nmm;t,mF`u$\"1yc*3 l')>!RF`u7$$\"1+]i!f#=$3#F`u$\"1)3$)eq\\'RVF`u7$$\"1+](=xpe=#F`u$\"1mo ffm-yZF`u7$$\"1nm\"H28IH#F`u$\"1Onc_*3zD&F`u7$$\"1n;zpSS\"R#F`u$\"1Zh, DM\")=dF`u7$$\"1LL3_?`(\\#F`u$\"1'e$=^jmPiF`u7$$\"1M$e*)>pxg#F`u$\"1*y N]>g/!oF`u7$$\"1+]Pf4t.FF`u$\"1eGo+6;5tF`u7$$\"1MLe*Gst!GF`u$\"1p.Ks\" R8)yF`u7$$\"1+++DRW9HF`u$\"11%p>R$)R\\)F`u7$$\"1++DJE>>IF`u$\"1+VfWT_: \"*F`u7$$\"1+]i!RU07$F`u$\"1\"f(o6[yP(*F`u7$$\"1++v=S2LKF`u$\"1G;2hnFX 5!#97$$\"1mmm\"p)=MLF`u$\"1)yjJU\"o66F\\\\l7$$\"1++](=]@W$F`u$\"1H1L\" zR[=\"F\\\\l7$$\"1L$e*[$z*RNF`u$\"1Y^5z`9`7F\\\\l7$$\"1,+]iC$pk$F`u$\" 1KOgQ;,I8F\\\\l7$$\"1m;H2qcZPF`u$\"1-TTZeU/9F\\\\l7$$\"1+]7.\"fF&QF`u$ \"1c7nq_P%[\"F\\\\l7$$\"1mm;/OgbRF`u$\"1K'Ht)*zYc\"F\\\\l7$$\"1+]ilAFj SF`u$\"1K(f/:=5l\"F\\\\l7$$\"1MLL$)*pp;%F`u$\"1,,?%)QOOF\\\\l7$$ \"1,++D>#[Z%F`u$\"1rg/EJS-?F\\\\l7$$\"1nmT&G!e&e%F`u$\"1+-SbYv-@F\\\\l 7$$\"1MLL$)Qk%o%F`u$\"1U_OJ))e%>#F\\\\l7$$\"1+]iSjE!z%F`u$\"1$[79;lYH# F\\\\l7$$\"1,]P40O\"*[F`u$\"1FtEj2a#R#F\\\\lFfq-%'COLOURG6&F4$\"*++++ \"FioF(F(-%*THICKNESSG6#FU-%&STYLEG6#%%LINEG-%+AXESLABELSG6$%\"xG%!G-% %VIEWG6$;F(Fgq%(DEFAULTG" 2 250 250 250 2 0 1 0 2 9 0 4 2 1.000000 45.000000 45.000000 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 1 }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "with(plots);" } }{PARA 12 "" 1 "" {XPPMATH 20 "6#7S%(animateG%*animate3dG%-changecoord sG%,complexplotG%.complexplot3dG%*conformalG%,contourplotG%.contourplo t3dG%*coordplotG%,coordplot3dG%-cylinderplotG%,densityplotG%(displayG% *display3dG%*fieldplotG%,fieldplot3dG%)gradplotG%+gradplot3dG%-implici tplotG%/implicitplot3dG%(inequalG%-listcontplotG%/listcontplot3dG%0lis tdensityplotG%)listplotG%+listplot3dG%+loglogplotG%(logplotG%+matrixpl otG%(odeplotG%'paretoG%*pointplotG%,pointplot3dG%*polarplotG%,polygonp lotG%.polygonplot3dG%.polyhedraplotG%'replotG%*rootlocusG%,semilogplot G%+setoptionsG%-setoptions3dG%+spacecurveG%1sparsematrixplotG%+spherep lotG%)surfdataG%)textplotG%+textplot3dG%)tubeplotG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{MARK "77 0 0" 0 }{VIEWOPTS 1 1 0 1 1 1803 }