Aulas Maple 2013.1

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aula4N.mws
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257 6 "Aula 4" }}{PARA 0 "" 0 "" {TEXT -1 20 "Turma 33N - 13.03.13" }}
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"" 0 "" {TEXT -1 26 "Definindo fun\347\365es no Maple" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "f:=x->x^2;" }}{PARA 11 "" 1 "" 
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\"F(F(F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 6 "f(-1);" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6#\"\"\"" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 13 "f(surd(2,4));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*$\"
\"##\"\"\"F$" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "f(x);" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#*$)%\"xG\"\"#\"\"\"" }}}{EXCHG {PARA 
0 "> " 0 "" {MPLTEXT 1 0 5 "f(w);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*
$)%\"wG\"\"#\"\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "g:=va
riavel->variavel^2;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"gGf*6#%)var
iavelG6\"6$%)operatorG%&arrowGF(*$)9$\"\"#\"\"\"F(F(F(" }}}{EXCHG 
{PARA 0 "" 0 "" {TEXT -1 99 "f e g s\343o a mesma fun\347\343o: `x` e \+
`variavel` s\343o apenas nomes que usamos para poder definir a fun\347
\343o." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 
0 "" 0 "" {TEXT -1 17 "Erro muito comum:" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 55 "h:=2*x+sqrt(x-1);#isso \351 uma express\343o e n\343o
 uma fun\347\343o" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"hG,&*&\"\"#\"
\"\"%\"xGF(F(*$,&F)F(F(!\"\"#F(F'F(" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 21 "h(4);#n\343o faz sentido" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#,&*&\"\"#\"\"\"-%\"xG6#\"\"%F&F&*$,&F'F&F&!\"\"#F&F%F&
" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "eval(h,x=4);#faz sentid
o" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,&\"\")\"\"\"*$\"\"$#F%\"\"#F%" }
}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 86 "eval \351 um comando que avalia \+
uma express\343o para um determinado valor de sua inc\363gnita." }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "expressao:=x^2+y^2;" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#>%*expressaoG,&*$)%\"xG\"\"#\"\"\"F**$
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{PARA 0 "" 0 "" {TEXT -1 21 "Exerc\355cio 1, lista 4." }}{PARA 0 "" 0 
"" {TEXT -1 129 "Defina a fun\347\343o V e determine um intervalo (com
 extremos aproximados) tal que se x pertence a esse intervalo, ent\343
o V(x)<sqrt(2)." }}}{EXCHG }{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "
h:=x->sqrt(36-4*x^2);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"hGf*6#%\"
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{PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "V(x);" }}{PARA 11 "" 1 "" {XPPMATH 
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aula5N.mws
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que o gr\341fico intersecta o eixo x em -2. N\343o confundir os eixos
 cartesianos com as laterais da janela de visualiza\347\343o." }}}
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!\"%" 1 2 0 1 10 0 2 9 1 4 2 1.000000 45.000000 48.000000 0 0 "Curve 1
" }}}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 260 "Como o m\355nimo est\341 na
 \372ltima janela plotada e como o \372ltimo intervalo de visualiza
\347\343o tem comprimento menor que 0.07, em particular, qualquer n
\372mero nesse intervalo ser\341 uma aproxima\347\343o do ponto de m
\355nimo (local) com erro menor que 0.07. Por exemplo, x=31.62." }}}
{EXCHG {PARA 0 "" 0 "" {TEXT -1 77 "Como garantir que o ponto de m\355
nimo local que encontramos \351, de fato, global?" }}}{EXCHG {PARA 0 "
> " 0 "" {MPLTEXT 1 0 18 "solve(P(x)<200.0);" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6$-%*RealRangeG6$,$%)infinityG!\"\"-%%OpenG6#$\"\"!F--F$6
$-F*6#$\"+am,F6!\")-F*6#$\"+YL)H())F4" }}}{EXCHG {PARA 0 "" 0 "" 
{TEXT -1 24 "Como fora do intervalo (" }{XPPEDIT 18 0 "11.27016654;" "
6#$\"+am,F6!\")" }{TEXT -1 2 ", " }{XPPEDIT 18 0 "88.72983346;" "6#$\"
+YL)H())!\")" }{TEXT -1 229 ") P(x) assume valores maiores que 200 ent
\341o, em particular, o ponto de m\355nimo global tem que estar nesse \+
intervalo. Como o primeiro intervalo plotado foi (0,100), ent\343o o \+
ponto de m\355nimo local que visualizamos era tamb\351m global." }}}
{EXCHG {PARA 0 "" 0 "" {TEXT -1 139 "Poder\355amos usar desse artif
\355cio desde o in\355cio: escolhemos um ponto no dom\355nio, por exem
plo, x=10 e perguntamos ao maple quando P(x)<P(10)." }}}{EXCHG {PARA 
0 "> " 0 "" {MPLTEXT 1 0 20 "solve(P(x)<P(10.0));" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6$-%*RealRangeG6$,$%)infinityG!\"\"-%%OpenG6#$\"\"!F--F$6
$-F*6#$\"#5F--F*6#$\"$+\"F-" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 113 "O
 ponto de m\355nimo global tem que estar no intervalo (10,100). Essa \+
seria uma boa escolha para a primeira janela." }}}}{MARK "27 0 0" 113 
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"" 0 "" {TEXT -1 23 "Continuando a aula 7..." }}}{EXCHG {PARA 0 "" 0 "
" {TEXT -1 7 "Lista 6" }}{PARA 0 "" 0 "" {TEXT -1 5 "ex. 9" }}{PARA 0 
"" 0 "" {TEXT -1 173 "Na m\343o, encontramos uma express\343o que forn
ece o comprimento da escada em fun\347\343o da dist\342ncia da cerca a
o p\351 da escada. O dom\355nio dessa fun\347\343o \351 (0,infinito) \+
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\"\"#F4F4*$),&\"#5F4*&\"#!)F4F3!\"\"F4F6F4F4F(F(F(" }}}{EXCHG {PARA 0 
"" 0 "" {TEXT -1 226 "Para estabelecermos, a priori, uma janela de vis
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emos um ponto no dom\355nio, por exemplo x=5, e perguntamos para que v
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{EXCHG {PARA 0 "" 0 "" {TEXT -1 580 "Como o m\355nimo encontra-se na \+
\372ltima janela plotada e a lateral horizontal da janela tem comprime
nto 0.01, ent\343o qualquer n\372mero nesse intervalo ser\341 uma apro
xima\347\343o do ponto de m\355nimo com erro menor que 0.01, em partic
ular, com erro menor que 0.07. Mas n\343o era isso que foi pedido,
ha
haha! Foi pedido uma aproxima\347\343o do menor tamanho da escada (ou \+
seja, uma aproxima\347\343o do valor m\355nimo da fun\347\343o). Mora
l da hist\363ria: pod\355amos ter parado h\341 muito tempo. 25.403 \+
\351 uma aproxima\347\343o do m\355nimo com erro menor que 0.0001 (que
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rmula xv=-b/2a, qual \351 o v\351rtice da par\341bola que \351 gr\341f
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" }}}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 2 "b)" }}}{EXCHG {PARA 0 "> " 0 
"" {MPLTEXT 1 0 8 "restart;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
18 "f:=x->-x^2+3*x-18;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"fGf*6#%
\"xG6\"6$%)operatorG%&arrowGF(,(*$)9$\"\"#\"\"\"!\"\"*&\"\"$F1F/F1F1\"
#=F2F(F(F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "x1:=solve(f(x
)=-20)[1];" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#x1G,&#\"\"$\"\"#\"\"
\"*&F(!\"\"\"#<#F)F(F+" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "x
2:=solve(f(x)=-20)[2];" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#x2G,&#\"
\"$\"\"#\"\"\"*&F(!\"\"\"#<#F)F(F)" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 14 "xv:=(x1+x2)/2;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#
xvG#\"\"$\"\"#" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 8 "ou ent\343o" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "with(student);" }}{PARA 12 "
" 1 "" {XPPMATH 20 "6#7@%\"DG%%DiffG%*DoubleintG%$IntG%&LimitG%(Linein
tG%(ProductG%$SumG%*TripleintG%*changevarG%/completesquareG%)distanceG
%'equateG%*integrandG%*interceptG%)intpartsG%(leftboxG%(leftsumG%)make
procG%*middleboxG%*middlesumG%)midpointG%(powsubsG%)rightboxG%)rightsu
mG%,showtangentG%(simpsonG%&slopeG%(summandG%*trapezoidG" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "completesquare(f(x));" }}{PARA 11 "
" 1 "" {XPPMATH 20 "6#,&*$),&%\"xG\"\"\"#\"\"$\"\"#!\"\"F+F(F,#\"#j\"
\"%F," }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 25 "o xv \351 3/2 e o yv \+
\351 -63/4" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG 
{PARA 0 "" 0 "" {TEXT -1 25 "Transforma\347\365es de gr\341fico" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart;" }}}{EXCHG {PARA 0 "
" 0 "" {TEXT -1 106 "Seja f uma fun\347\343o com gr\341fico conhecido.
 Podemos a partir do gr\341fico da f, esbo\347ar o gr\341fico das fun
\347\365es:" }}{PARA 0 "" 0 "" {TEXT -1 61 "i) g(x)=f(x-c) \+
 #deslocamento horizontal" }}{PARA 0 "" 0 "" {TEXT -1 58 "ii
) g(x)=f(x)+c #deslocamento vertical" }}{PARA 0 "
" 0 "" {TEXT -1 48 "iii) g(x)=f(cx), com 0<c<1 #expans\343o horizonta
l" }}{PARA 0 "" 0 "" {TEXT -1 50 "iv) g(x)=f(cx), com c>1 #contra
\347\343o horizontal" }}{PARA 0 "" 0 "" {TEXT -1 56 "v) g(x)=f(-x), \+
 #reflex\343o horizontal" }}{PARA 0 "" 0 "" {TEXT 
-1 54 "vi) g(x)=-f(x), #reflex\343o vertical" }}}
{EXCHG {PARA 0 "" 0 "" {TEXT -1 59 "Considere a seguinte fun\347\343o,
 definida no intervalo [-2 , 2]" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 13 "f:=x->-x^3+x;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"fGf*6#%\"
xG6\"6$%)operatorG%&arrowGF(,&*$)9$\"\"$\"\"\"!\"\"F/F1F(F(F(" }}}
{EXCHG {PARA 0 "" 0 "" {TEXT -1 24 "Vamos plotar as fun\347\365es:" }}
}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "g1:=x->f(x-2);" }}{PARA 11 
"" 1 "" {XPPMATH 20 "6#>%#g1Gf*6#%\"xG6\"6$%)operatorG%&arrowGF(-%\"fG
6#,&9$\"\"\"\"\"#!\"\"F(F(F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 16 "g2:=x->3*f(x+1);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#g2Gf*6#%
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(F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "g3:=x->-f(x);" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#g3Gf*6#%\"xG6\"6$%)operatorG%&arrow
GF(,$-%\"fG6#9$!\"\"F(F(F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
13 "g4:=x->f(-x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#g4Gf*6#%\"xG6
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{MPLTEXT 1 0 29 "G1:=plot(g1,0..4,color=blue):" }}}{EXCHG {PARA 0 "> \+
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{PARA 0 "> " 0 "" {MPLTEXT 1 0 31 "G3:=plot(g3,-2..2,color=green):" }}
}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 33 "G4:=plot(g4,-2..2,color=mag
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1,color=\"HotPink\"):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 38 "di
splay(F,G1,G2,G3,G4,G5,thickness=3);" }}{PARA 13 "" 1 "" {GLPLOT2D 
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start;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 37 "f:=x->x*(x^2-1):g
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3/2;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#xDG#\"\"$\"\"#" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "yD:=f(3/2);" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>%#yDG#\"#:\"\")" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 7 "yC:=yD;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#yCG#\"#:\"\")" }}
}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "solve(g(x)=yC);" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6$,&\"\"%\"\"\"*&F$!\"\"\"\"'#F%\"\"#F',&F$F%*
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{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 9 "Determine" }
}{PARA 0 "" 0 "" {TEXT -1 29 "a) as coordenadas do ponto C." }}}
{EXCHG {PARA 0 "" 0 "" {TEXT -1 13 "Resposta: C=(" }{XPPEDIT 18 0 "4+1
/4*6^(1/2);" "6#,&\"\"%\"\"\"*&F$!\"\"\"\"'#F%\"\"#F%" }{TEXT -1 6 ",1
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"> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 28 "b) \+
a \341rea do ret\342ngulo ABCD." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 27 "largura:=4+1/4*6^(1/2)-3/2;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6
#>%(larguraG,&#\"\"&\"\"#\"\"\"*&\"\"%!\"\"\"\"'#F)F(F)" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "altura:=15/8;" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>%'alturaG#\"#:\"\")" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 21 "area:=largura*altura;" }}{PARA 11 "" 1 "" {XPPMATH 
20 "6#>%%areaG,&#\"#v\"#;\"\"\"*(\"#:F)\"#K!\"\"\"\"'#F)\"\"#F)" }}}
{EXCHG {PARA 0 "" 0 "" {TEXT -1 130 "3)Seja f uma fun\347\343o cujo gr
\341fico \351 uma par\341bola. Sabendo que f(x) = 0 se e somente se x \+
= -1\nou x = 4, e que f(0) = -2, determine:" }}}{EXCHG {PARA 0 "" 0 "
" {TEXT -1 20 "a) a express\343o de f." }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 8 "restart;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 
"f:=x->a*(x-4)*(x+1);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"fGf*6#%\"
xG6\"6$%)operatorG%&arrowGF(*(%\"aG\"\"\",&9$F.\"\"%!\"\"F.,&F0F.F.F.F
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;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6##\"\"\"\"\"#" }}}{EXCHG {PARA 0 "
> " 0 "" {MPLTEXT 1 0 0 "" }}{PARA 11 "" 1 "" {TEXT -1 0 "" }}}{EXCHG 
{PARA 0 "" 0 "" {TEXT -1 19 "A express\343o \351 f(x)=" }{XPPEDIT 18 
0 "1/2*(x-4)*(x+1);" "6#,$*(\"\"#!\"\",&%\"xG\"\"\"\"\"%F&F),&F(F)F)F)
F)F)" }{TEXT -1 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 111 "b) a taxa
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 primeira coordenada do\nv\351rtice da par\341bola." }}}{EXCHG {PARA 
0 "> " 0 "" {MPLTEXT 1 0 14 "with(student):" }}}{EXCHG {PARA 0 "> " 0 
"" {MPLTEXT 1 0 22 "F:=x->1/2*(x-4)*(x+1);" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>%\"FGf*6#%\"xG6\"6$%)operatorG%&arrowGF(,$*&#\"\"\"\"
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{XPPMATH 20 "6#,&*&\"\"#!\"\",&%\"xG\"\"\"#\"\"$F%F&F%F)#\"#D\"\")F&" 
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"" {XPPMATH 20 "6#>%#xvG#\"\"$\"\"#" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 27 "taxa:=(F(xv)-F(-1))/(xv+1);" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>%%taxaG#!\"&\"\"%" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 
16 "c) a imagem de f" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 106 "O gr\341
fico \351 uma par\341bola com a concavidade virada para cima. Assim, \+
a imagem da fun\347\343o ser\341 [yv,infinito)" }}}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 10 "yv:=F(xv);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#
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/8, infinito)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}
{EXCHG {PARA 0 "" 0 "" {TEXT -1 211 "4) Seja R um ret\342ngulo de base
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ea 12 deve ser constru\355do dentro do ret\342ngulo R de forma que sua
 base AB fique sobre a base do ret\342ngulo R. Seja x= AB." }}{PARA 
0 "" 0 "" {TEXT -1 105 "a) Determine o dom\355nio e a express\343o da \+
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\347\343o de x." }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 119 "Pelas restri
\347\365es das dimens\365es do ret\342ngulo e da rela\347\343o entre a
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{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "h:=x->24/x;" }}{PARA 11 "" 
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}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 240 "Como o \372ltimo intervalo plot
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{TEXT -1 165 "Quando usamos a representa\347\343o decimal de um n\372m
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{EXCHG {PARA 0 "" 0 "" {TEXT -1 46 "O s\355mbolo % indica o \372ltimo \+
comando executado." }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 81 "H\341 uma o
utra maneira de extrair a ra\355z n-\351sima de um n\372mero: usar o c
omando surd." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "surd(10^(-4
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0 "" 0 "" {TEXT -1 2 "5)" }}{PARA 0 "" 0 "" {TEXT -1 92 "O comando sim
plify pode ser usado para simplificarmos express\365es aritm\351ticas
 ou alg\351bricas." }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 2 "a)" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "simplify(5*x-(x+2)/3);" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#,&*(\"#9\"\"\"\"\"$!\"\"%\"xGF&F&#\"\"
#F'F(" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 2 "b)" }}}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 54 "simplify(sqrt(3)/2+2*sqrt(27)/3-(sqrt(3/4)+sqr
t(12)));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"!" }}}{EXCHG {PARA 0 "
" 0 "" {TEXT -1 34 "6) Resolvendo equa\347\365es no Maple..." }}}
{EXCHG {PARA 0 "" 0 "" {TEXT -1 2 "b)" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 21 "solve(1-(x+2)/3=x/2);" }}{PARA 11 "" 1 "" {XPPMATH 
20 "6##\"\"#\"\"&" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 6 "2/5*n;
" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,$*(\"\"#\"\"\"\"\"&!\"\"%\"nGF&F&
" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 256 "O argumento do solve deve se
r sempre uma equa\347\343o (ou um sistema ou uma inequa\347\343o). O \+
maple convenciona que ao colocarmos uma express\343o no argumento do s
olve, estamos a procura dos zeros da express\343o. Entretanto, nesse \+
curso, n\343o admitiremos essa sintaxe." }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 23 "solve(3*x+2=0);#correto" }}{PARA 11 "" 1 "" {XPPMATH 
20 "6##!\"#\"\"$" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "solve(3
*x+2);#errado" }}{PARA 11 "" 1 "" {XPPMATH 20 "6##!\"#\"\"$" }}}
{EXCHG {PARA 0 "" 0 "" {TEXT -1 27 "Fa\347am os itens e, h, j e k." }}
}{EXCHG {PARA 0 "" 0 "" {TEXT -1 2 "e)" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 36 "solve( (y^2-4*y+4)/(6*y^2-12*y)=0 );" }}}{EXCHG 
{PARA 0 "" 0 "" {TEXT -1 183 "Verificamos na m\343o que quando o numer
ador da express\343o zera (y=2), o denominador zera tamb\351m. Dessa f
orma, n\343o pode haver solu\347\343o e, por isso, o maple n\343o apre
senta nenhuma resposta. " }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 2 "h)" }}
}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "solve(9*x^2-6*x+1=0);" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6$#\"\"\"\"\"$F#" }}}{EXCHG {PARA 0 "" 
0 "" {TEXT -1 113 "Se a ra\355z tem multiplicidade maior que um, o map
le repete ela na resposta quantas vezes for a sua multiplicidade." }}}
{EXCHG {PARA 0 "" 0 "" {TEXT -1 2 "j)" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 21 "solve(9*x^2-6*x+6=0);" }}{PARA 11 "" 1 "" {XPPMATH 
20 "6$,&#\"\"\"\"\"$F%*&^#F$F%\"\"&#F%\"\"#F%,&F$F%*&^##!\"\"F&F%F)F*F
%" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 160 "O maple retornou dois n\372
mero complexos n\343o reais. Nesse curso, trabalharemos apenas com n
\372meros reais e, portanto, para n\363s, essa equa\347\343o n\343o po
sssui solu\347\343o. " }}}{EXCHG {PARA 0 ""
0 "" {TEXT -1 2 "k)" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "solve(x^3+x^2+20=(x+4)*(x+5)
);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"\"!\"\"$!\"$" }}}{EXCHG {PARA 
0 "" 0 "" {TEXT -1 2 "8)" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 2 "a)" }}
}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 71 "simplify((x^5-3/2*x^4-48*x^
3+409/2*x^2-174*x-144)/(x^3-4*x^2+10*x-21));" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#,$*(\"\"#!\"\",,*&F%\"\"\")%\"xG\"\"%F)F)*&\"\"$F))F+F.
F)F)*&\"#()F))F+F%F)F&*&\"$[\"F)F+F)F)\"#'*F)F),(*$F2F)F)F+F&\"\"(F)F&
F)" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 330 "Aqui devemos tomar cuidado
. Para todo o valor de x em que a express\343o original pode ser aval
iada, os valores das duas express\365es s\343o iguais. Entretanto, ex
iste um valor de x em que a segunda express\343o pode ser avaliada, ma
s a primeira n\343o. Para garantirmos que as express\365es s\343o igu
ais, devemos incluir a restri\347\343o na resposta." }}}{EXCHG {PARA 
0 "> " 0 "" {MPLTEXT 1 0 47 "factor(x^5-3/2*x^4-48*x^3+409/2*x^2-174*x
-144);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,$*,\"\"#!\"\",&%\"xG\"\"\"
\"\")F)F),&F(F)\"\"%F&F),&*&F%F)F(F)F)F)F)F),&F(F)\"\"$F&F%F)" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "factor(x^3-4*x^2+10*x-21);" 
}}{PARA 11 "" 1 "" {XPPMATH 20 "6#*&,&%\"xG\"\"\"\"\"$!\"\"F&,(*$)F%\"
\"#F&F&F%F(\"\"(F&F&" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}
}{EXCHG {PARA 0 "" 0 "" {TEXT -1 237 "O polin\364mio (x-3) \351 um fat
or comum do numerador e do denominador. A segunda express\343o (simpl
ificada) cancelou esses fatores. Para que as express\365es sejam igua
is, \351 necess\341rio incluir a restri\347\343o \"x diferente de 3\" \+
na segunda express\343o." }}{PARA 0 "" 0 "" {TEXT -1 9 "Resposta:" }
{XPPEDIT 18 0 "1/2*(2*x^4+3*x^3-87*x^2+148*x+96)/(x^2-x+7);" "6#*(\"\"
#!\"\",,*&F$\"\"\")%\"xG\"\"%F(F(*&\"\"$F()F*F-F(F(*&\"#()F()F*F$F(F%*
&\"$[\"F(F*F(F(\"#'*F(F(,(*$F1F(F(F*F%\"\"(F(F%" }{TEXT -1 20 " e x di
ferente de 3." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}
{EXCHG {PARA 0 "" 0 "" {TEXT -1 218 "Quando uma equa\347\343o tem mais
 de uma inc\363gnita e queremos resolv\352-la para uma das inc\363gnit
as (ou seja, quando queremos isolar uma das inc\363gnitas), [e necess
\341rio avisar o maple qual das inc\363gnitas \351 a vari\341vel da eq
ua\347\343o." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "solve(a*x^2
+b*x+c=0,x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$,$*(\"\"#!\"\",&%\"bG
\"\"\"*$,&*$)F(F%F)F)*(\"\"%F)%\"aGF)%\"cGF)F&#F)F%F&F)F0F&F&,$*(F%F&,
&F(F)F*F)F)F0F&F&" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 67 "\311 poss
\355vel resolver um sistema de equa\347\365es no maple usando o solve:
" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 3 "6c)" }}}{EXCHG {PARA 0 "> " 0 
"" {MPLTEXT 1 0 28 "solve(\{2*x+5=y+10,y-3=x-4\});" }}{PARA 11 "" 1 "
" {XPPMATH 20 "6#<$/%\"yG\"\"$/%\"xG\"\"%" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 34 "solve(\{a*x+5=y+10,y-3=x-4\},\{x,y\});" }}{PARA 11 
"" 1 "" {XPPMATH 20 "6#<$/%\"yG,$*&,&%\"aG\"\"\"F*!\"\"F+,&F)F*\"\"&F+
F*F+/%\"xG,$*&\"\"%F*F(F+F*" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 55 "O \+
solve pode ser usado tamb\351m para resolver inequa\347\365es:" }}}
{EXCHG {PARA 0 "" 0 "" {TEXT -1 3 "11)" }}{PARA 0 "" 0 "" {TEXT -1 2 "
a)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 32 "solve(3*(1-x)+7*x<33-
4*(5-2*x));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%*RealRangeG6$-%%OpenG
6##!\"&\"\"#%)infinityG" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 108 "Quand
o a extremidade do intervalo solu\347\343o \351 aberta o maple escreve
 `open`, caso contr\341rio, n\343o escreve nada." }}}{EXCHG {PARA 0 "
" 0 "" {TEXT -1 2 "b)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "so
lve(-4<2-3*x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%*RealRangeG6$,$%)i
nfinityG!\"\"-%%OpenG6#\"\"#" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 17 "solve(2-3*x<=17);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%*RealRang
eG6$!\"&%)infinityG" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 66 "Tomando a \+
interse\347\343o das duas solu\347\365es obtemos o intervalo [-5,2)." 
}}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 2 "c)" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 25 "solve((2*x-5)*(-x+4)<=0);" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6$-%*RealRangeG6$,$%)infinityG!\"\"#\"\"&\"\"#-F$6$\"\"%F
'" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 81 "O maple n\341o indica a uni
\343o dos intervalos, apenas os separa por v\355rgula. Solu\347\343o:
" }}{PARA 0 "" 0 "" {TEXT -1 29 "(-infinito,5/2]U[4,infinito)." }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" 
{TEXT -1 102 "Para procurar no help informa\347\365es sobre um determi
nado comando, digite na linha de comando: ?[comando]" }}}{EXCHG {PARA 
0 "> " 0 "" {MPLTEXT 1 0 6 "?solve" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 56 "Esqueci de um
 comando: expand. \311 o contr\341rio do factor." }}}{EXCHG {PARA 0 "
> " 0 "" {MPLTEXT 1 0 31 "expand((x-3)*(x^2+5)*(-1+x^3));" }}{PARA 11 
"" 1 "" {XPPMATH 20 "6#,0*&\"#;\"\"\")%\"xG\"\"$F&!\"\"*$)F(\"\"'F&F&*
&\"\"&F&F(F&F**&F/F&)F(\"\"%F&F&*&F)F&)F(\"\"#F&F&*&F)F&)F(F/F&F*\"#:F
&" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{MARK "93 0 0" 0 
}{VIEWOPTS 1 1 0 3 2 1804 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }
aula2N.mws
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{EXCHG {PARA 0 "" 0 "" {TEXT -1 70 "\311 poss\355vel pedir ao maple a \+
expans\343o decimal de um determinado n\372mero." }}}{EXCHG {PARA 0 ">
 " 0 "" {MPLTEXT 1 0 6 "1.0/3;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+
LLLLL!#5" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "evalf(1/3);" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+LLLLL!#5" }}}{EXCHG {PARA 0 "> " 
0 "" {MPLTEXT 1 0 10 "evalf(Pi);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$
\"+aEfTJ!\"*" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 110 "Pi deve ser escr
ito com p mai\372sculo, caso contr\341rio o maple entende que estamos \+
apenas usando uma letra grega." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 26 "pi;#apenas uma letra grega" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#
%#piG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "evalf(pi);" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#%#piG" }}}{EXCHG {PARA 0 "" 0 "" 
{TEXT -1 93 "Embora o padr\343o do Maple seja usar 10 d\355gitos, pode
mos mudar esse padr\343o com o comando Digits" }}}{EXCHG {PARA 0 "> " 
0 "" {MPLTEXT 1 0 11 "Digits:=50;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>
%'DigitsG\"#]" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "evalf(Pi);
" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"S^P*Rpr>%)G]zKQVEYQKz*e`EfTJ!#
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{PARA 11 "" 1 "" {XPPMATH 20 "6#>%'DigitsG\"$+#" }}}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 10 "evalf(Pi);" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#
$\"cw?QI\\&*[HiW'fb5@&Q>q-TG]u6\"[G\"3%f`sJAe]&4Y%Q4ZmI#G8l3[@)z1<@MD[
.G')**3iG1k\"yI#fW\\(4#e5v$*Rpr>%)G]zKQVEYQKz*e`EfTJ!$*>" }}}{EXCHG 
{PARA 0 "" 0 "" {TEXT -1 172 "O truncamento de um n\372mero com n casa
s decimais \351 a expans\343o decimal desse n\372mero at\351 a n-\351s
ima casa decimal. Por exemplo o truncamento de Pi com 4 casas decimais
 \351 3,1415." }}{PARA 0 "" 0 "" {TEXT -1 16 "Uma aproxima\347\343o " 
}{TEXT 258 2 "a " }{TEXT -1 34 "de um n\372mero x com erro menor que \+
" }{TEXT 259 1 "e" }{TEXT -1 24 " \351 um n\372mero tal que |x-" }
{TEXT 260 1 "a" }{TEXT -1 2 "|<" }{TEXT 261 2 "e," }{TEXT -1 33 " ou, \+
equivalentemente, tal que x-" }{TEXT 262 1 "e" }{TEXT -1 1 "<" }{TEXT 
264 1 "a" }{TEXT -1 3 "<x+" }{TEXT 263 2 "e." }}}{EXCHG {PARA 0 "> " 
0 "" {MPLTEXT 1 0 8 "restart;" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 106 
"O truncamento de um n\372mero com n casas decimais \351 uma aproxima
\347\343o desse n\372mero com erro menor que 10^(-n)." }}}{EXCHG 
{PARA 0 "" 0 "" {TEXT -1 53 "D\352 uma aproxima\347\343o de Pi com err
o menor que 10^(-10)." }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 140 "Para re
sponder esse tipo de pergunta no Maple, primeiro aumente o padr\343o d
o n\372mero de d\355gitos (para um n\372mero suficientemente maior que
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{PARA 11 "" 1 "" {XPPMATH 20 "6#>%'DigitsG\"#:" }}}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 10 "evalf(Pi);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#
$\"0z*e`EfTJ!#9" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "3.141592
65358979; #correto" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"0z*e`EfTJ!#9
" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "3.14159265358; #correto
" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"-e`EfTJ!#6" }}}{EXCHG {PARA 0 "
> " 0 "" {MPLTEXT 1 0 22 "3.1415926535; #correto" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#$\",Nl#fTJ!#5" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 28 "evalf(abs(Pi-3.1415926535));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#
$\"%z*)!#9" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 49 "abs \351 o comando \+
usado para valor absouto (m\363dulo)" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 28 "evalf(abs(3.1415926536-Pi));" }}{PARA 11 "" 1 "" 
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aula3N.mws
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{SECT 0 {EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }{TEXT 256 0 "" }{TEXT 
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}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart;" }}}{EXCHG {PARA 0 
"" 0 "" {TEXT -1 103 "Podemos definir uma sequ\352ncia explicitamente,
 a partir de uma express\343o que depende de n. Por exemplo, " }
{XPPEDIT 18 0 "a[n];" "6#&%\"aG6#%\"nG" }{TEXT -1 190 "=3n+4. Entretan
to podemos definir essa mesma sequ\352ncia de forma recursiva, ou seja
, definimos o primeiro termo da sequ\352ncia e uma f\363rmula que rela
ciona o termo seguinte a partir do anterior." }}{PARA 0 "" 0 "" 
{XPPEDIT 18 0 "a[1] = 7;" "6#/&%\"aG6#\"\"\"\"\"(" }{TEXT -1 0 "" }}
{PARA 0 "" 0 "" {XPPEDIT 18 0 "a[n+1] = a[n]+3;" "6#/&%\"aG6#,&%\"nG\"
\"\"F)F),&&F%6#F(F)\"\"$F)" }{TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 65 "Como podemo
s construir essa sequ\352ncia no maple? Usando o comando " }{TEXT 258 
4 "for." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "a[1]:=7;" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%\"aG6#\"\"\"\"\"(" }}}{EXCHG {PARA 
0 "> " 0 "" {MPLTEXT 1 0 75 "for i from 1 to 50 do #[shift+enter]\na[i
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6#>&%\"aG6#\"\"#\"#5" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%\"aG6#\"\"$
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mo e m\355nimo global s\343o os pontos de derivada nula e os extremos \+
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"solve(D(d)(x)=0);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"\"&,&F#\"\"\"*
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x4:=5+sqrt(66);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#x4G,&\"\"&\"\"\"
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a do dom\355nio. Conforme x cresce arbitrariamente, o valor da fun\347
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{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"!" }}}{EXCHG {PARA 0 "" 0 "" 
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