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{SECT 0 {EXCHG {PARA 259 "" 0 "" {TEXT -1 20 "AULA 3  (28/05/2002)" }}
{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 4 "" 0 "" {TEXT -1 27 "LABORAT
\323RIO  DE MATEM\301TICA " }}{PARA 4 "" 0 "" {TEXT -1 41 "2.3 Trabalh
ando com express\365es alg\351bricas" }}{PARA 4 "" 0 "" {TEXT -1 37 "A
tribui\347\343o de um nome a uma express\343o" }}{PARA 0 "" 0 "" 
{TEXT -1 1 " " }{TEXT 256 197 "Uma express\343o n\343o precisa necessa
riamente ter nome, por\351m algumas vezes \351 melhor nomea-las, pois \+
isso muitas vezes facilita o trabalho, principalmente quando precisamo
s utilizar-la diversas vezes. " }}{PARA 0 "" 0 "" {TEXT -1 7 "Exemplo
" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "eq:= 3*x^2+2*x-1=0;" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#eqG/,(*$%\"xG\"\"#\"\"$F(F)!\"\"\"
\"\"\"\"!" }}}{PARA 0 "" 0 "" {TEXT 257 25 " Alguns comandos b\341sico
s:" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "" 0 "" {TEXT 
260 6 "Expand" }{TEXT 295 2 ": " }{TEXT 266 10 "O comando " }{TEXT 
259 8 " \"expand" }{TEXT 261 117 " \" serve para expandir express\365e
s incluindo tamb\351m  express\365es na forma trigonom\351trica, logar
\355tmica etc. Por exemplo:" }}{PARA 0 "" 0 "" {TEXT 262 107 "Uma expr
ess\343o dada na forma fatorada, permanece nesta forma at\351 que sua \+
expans\343o seja pedida, e vice-versa:" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 8 "(x-1)^5;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*$,&%\"xG
\"\"\"!\"\"F&\"\"&" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "expan
d(\");" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,.*$%\"xG\"\"&\"\"\"*$F%\"\"
%!\"&*$F%\"\"$\"#5*$F%\"\"#!#5F%F&!\"\"F'" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 10 "factor(\");" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*$,&
%\"xG\"\"\"!\"\"F&\"\"&" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 42 "
cos(alpha+beta) = expand(cos(alpha+beta));" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#/-%$cosG6#,&%&alphaG\"\"\"%%betaGF),&*&-F%6#F(F)-F%6#F*
F)F)*&-%$sinGF.F)-F3F0F)!\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 38 "ln(3*x^2*y^2) = expand(ln(3*x^2*y^2));" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#/-%#lnG6#,$*&%\"xG\"\"#%\"yGF*\"\"$,(-F%6#F,\"\"\"-F%6#
F)F*-F%6#F+F*" }}}{EXCHG {PARA 256 "" 0 "" {TEXT -1 8 "Simplify" }}
{PARA 0 "" 0 "" {TEXT 268 10 "O comando " }{TEXT 263 8 "simplify" }
{TEXT 269 451 " \351 um comando geral de simplifica\347\343o. A primei
ra coisa que ele faz \351 procurar dentro da express\343o a ocorr\352n
cia de fun\347\365es matem\341ticas, quando encontra usa as propriedad
es de simplifica\347\343o destas fun\347\365es, como por exemplo ra
\355zes quadradas,  radicais e  pot\352ncias. No entanto, \351 poss
\355vel aplicar as regras de simplifica\347\343o de determinadas fun
\347\365es de maneira selecionada. Para isso deve-se dar o nome da fun
\347\343o em quest\343o no segundo argumento do comando " }{TEXT 264 
8 "simplify" }{TEXT 270 39 ", que pode ser um dos seguintes nomes: " }
{TEXT 265 53 "trig, hypergeom, radical, power, exp, ln, sqrt, etc. " }
}{PARA 0 "" 0 "" {TEXT 267 9 "Exemplos:" }}{PARA 0 "> " 0 "" {MPLTEXT 
1 0 20 "a:=((x^2-16)/(x+4));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"aG
*&,&*$%\"xG\"\"#\"\"\"!#;F*F*,&F(F*\"\"%F*!\"\"" }}}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 14 "simplify((a));" }}{PARA 11 "" 1 "" {XPPMATH 
20 "6#,&%\"xG\"\"\"!\"%F%" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
33 "simplify((x^a)^b+4^(1/2), power);" }}{PARA 11 "" 1 "" {XPPMATH 20 
"6#,&))%\"xG%\"aG%\"bG\"\"\"\"\"#F)" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 
271 5 "Solve" }}{PARA 0 "" 0 "" {TEXT 272 104 "Com esse comando obt
\351m-se a solu\347\343o de equa\347\365es, algumas vezes dif\355ceis \+
de serem resolvidas manualmente." }}{PARA 0 "" 0 "" {TEXT 273 15 "A se
qu\352ncia \351: " }{TEXT 274 23 "solve(equa\347\343o,vari\341vel)" }}
{PARA 0 "" 0 "" {TEXT 275 3 "Ex." }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 21 
"solve(x^3-2*x^2-x,x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"\"!,&*$\"
\"##\"\"\"F&F(F(F(,&F(F(F%!\"\"" }}}{PARA 0 "" 0 "" {TEXT 258 96 " Com
 o comando solve voc\352 pode tamb\351m solucionar sistemas de v\341ri
as equa\347\365es e v\341rias inc\363gnitas" }}{PARA 0 "" 0 "" {TEXT 
276 8 "Exemplo:" }}{PARA 0 "" 0 "" {TEXT 277 77 "Nesse caso conv\351m \+
atribuir um nome as express\365es, para depois pedir a solu\347\343o" 
}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 42 "eqns := \{x+y+2*z=1, 3*x+2
*y=2, x-2*y-z=0\};" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%eqnsG<%/,(%\"
xG\"\"\"%\"yGF)%\"zG\"\"#F)/,&F(\"\"$F*F,F,/,(F(F)F*!\"#F+!\"\"\"\"!" 
}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "solve( eqns );" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6#<%/%\"yG#\"\"\"\"\"&/%\"xG#\"\")\"#:/%\"zG#
\"\"#F-" }}}{EXCHG {PARA 257 "" 0 "" {TEXT 278 9 "Subs   - " }{TEXT 
279 63 " Esse comando serve para substituir subexpress\365es em expres
s\365es" }}{PARA 0 "" 0 "" {TEXT 280 9 "Exemplos:" }}{PARA 0 "> " 0 "
" {MPLTEXT 1 0 28 "subs( x=1/3, x^3+2*x^2-x+5);" }}{PARA 0 "" 0 "" 
{TEXT -1 0 "" }}{PARA 11 "" 1 "" {XPPMATH 20 "6##\"$L\"\"#F" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "subs(x=a^2+1,3*x+21);" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#,&*$%\"aG\"\"#\"\"$\"\"%\"\"\"" }}}
{EXCHG {PARA 258 "" 0 "" {TEXT 281 10 "Sum   -   " }{TEXT 282 42 "Calc
ula somat\363rios definidos e indefinidos" }}{PARA 0 "" 0 "" {TEXT 
283 10 "Exemplos: " }}{PARA 0 "" 0 "" {TEXT 284 1 " " }}}{EXCHG {PARA 
0 "> " 0 "" {MPLTEXT 1 0 23 "sum('k^3+2', 'k'=0..4);" }}{PARA 11 "" 1 
"" {XPPMATH 20 "6#\"$5\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 
"sum('k^3+2', 'k'=0..n);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,,*$,&%\"n
G\"\"\"F'F'\"\"%#F'F(*$F%\"\"$#!\"\"\"\"#*$F%F.F)F&F.F.F'" }}}{PARA 0 
"" 0 "" {TEXT 285 29 "Usando o s\355mbolo de somat\363rio" }}{PARA 0 "
" 0 "" {TEXT 286 3 "Ex." }}{PARA 0 "" 0 "" {TEXT 287 1 " " }}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "Sum('a[k]','k'=0..10);" }}{PARA 11 
"" 1 "" {XPPMATH 20 "6#-%$SumG6$&%\"aG6#%\"kG/F);\"\"!\"\"%" }}}
{EXCHG {PARA 0 "" 0 "" {TEXT 288 55 "Para obter o resultado da soma , \+
toma-se o s min\372sculo." }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "sum('a
[k]','k'=0..5);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,8&%\"aG6#\"\"!\"\"
\"&F%6#F(F(&F%6#\"\"#F(&F%6#\"\"$F(&F%6#\"\"%F(&F%6#\"\"&F(&F%6#\"\"'F
(&F%6#\"\"(F(&F%6#\"\")F(&F%6#\"\"*F(&F%6#\"#5F(" }}}{EXCHG {PARA 0 "
" 0 "" {TEXT 289 8 "Ou ainda" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 42 "Sum
('a[k]','k'=0..5)=sum('a[k]','k'=0..5);" }}{PARA 11 "" 1 "" {XPPMATH 
20 "6#/-%$SumG6$&%\"aG6#%\"kG/F*;\"\"!\"\"&,.&F(6#F-\"\"\"&F(6#F2F2&F(
6#\"\"#F2&F(6#\"\"$F2&F(6#\"\"%F2&F(6#F.F2" }}}{EXCHG {PARA 0 "" 0 "" 
{TEXT 290 7 "Product" }}{PARA 0 "" 0 "" {TEXT 291 40 "Calcula produtos
 definidos e indefinidos" }}{PARA 0 "" 0 "" {TEXT 292 9 "Exemplos:" }}
{PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "product( k^3, k=1..4 );" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6#\"&CQ\"" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 23 "product( k^3, k=1..n );" }}{PARA 11 "" 1 "" {XPPMATH 
20 "6#*$-%&GAMMAG6#,&%\"nG\"\"\"F)F)\"\"$" }}}{EXCHG {PARA 0 "" 0 "" 
{TEXT 293 27 "Usando o s\355mbolo de produto" }}{PARA 0 "" 0 "" {TEXT 
294 4 "Ex. " }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "product( a[k], k=0..
n );" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%(productG6$&%\"aG6#%\"kG/F);
\"\"!%\"nG" }}}}{MARK "12 0 0" 0 }{VIEWOPTS 1 1 0 1 1 1803 }
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