puc Segunda Prova de Calculo Numerico 2018
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puc Segunda Prova de Calculo Numerico 2018


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Pontifícia Universidade Católica de Minas Gerais \u2013 PUC-MG 
Departamento de Matemática e Estatística \u2013 DME - Prof. Pedro Américo Jr. 
Cálculo Numérico \u2013 Segunda Prova 
Aluno: Thaís Gabrielle Alves Oliveira Turma:__________ 
 
1) Ajuste os pontos abaixo a expressão (\uf078\uf0a310-4): 
 
)(log 214 cxbxay \uf02b\uf02b\uf03d
 
X1 1 2 3 4 5 
X2 2 5 3 1 2 
Y 1,08502 2,29248 2,16096 2,0000 2,19616 
 
 
 
RESPOSTA: 0,3832 + 0,2966X1 + 0,291 
 
2) Revolver o P.V.I (\uf078\uf0a310-4): 
\uf05b \uf05d )(5,1;5,01,0
1)1(
4)1(
2)1(
2
xyexmalhaehcom
y
y
y
yxy
\uf0ce\uf03d
\uf0ef
\uf0ef
\uf0ee
\uf0ef
\uf0ef
\uf0ed
\uf0ec
\uf02d\uf03d\uf0a2\uf0a2
\uf03d\uf0a2
\uf03d
\uf0a2\uf02d\uf02b\uf03d\uf0a2\uf0a2\uf0a2
 
 
 
 
 
3) Resolva o sistema de equações diferenciais (\uf078\uf0a310-6) 
 
4) Resolver o sistema linear complexo (\uf078\uf0a310-4): 
\uf05b \uf05d2,0 ;0,0 1,0 ,)( ),(
10)0( ,5
)0(
 , 2573
2)0( ,14
)0(
 , )(75
2
2
2
2
\uf0ce\uf03d\uf044
\uf0ef
\uf0ef
\uf0ee
\uf0ef
\uf0ef
\uf0ed
\uf0ec
\uf03d\uf03d\uf03d\uf02d\uf02d\uf02b
\uf03d\uf03d\uf03d\uf02b\uf02b\uf02b
tmalhattytx
y
dt
dy
yx
dt
dy
dt
yd
x
dt
dx
xysenxy
dt
dx
dt
xd
 
\uf0ef
\uf0ee
\uf0ef
\uf0ed
\uf0ec
\uf02d\uf03d\uf02d\uf02b
\uf02d\uf02d\uf03d\uf02b\uf02b\uf02d\uf02d
\uf02b\uf03d\uf02b\uf02b\uf02d
ixxx
ixixix
ixxixi
422
21)21(2
41)1(
321
321
321
 
 
5) Encontre todas as raízes reais da equação 
x7-7,4x6+13,83x5+12,604x4-55,4369x3+20,6631x2+49,412025x-35,1351=0, com \uf065 \uf0a3 10-8. 
 
 
6) Calcule todas as raízes reais de:
0,0000001 com 05 2/23 \uf0a3\uf03d\uf02b\uf02d \uf065xexx . 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
7) Ajuste os pontos abaixo a expressão (\uf078a\uf0a310
-5): 
 
8) Complete a tabela abaixo (\uf078a\uf0a310
-4) : 
\uf05b \uf05d\uf0ef\uf0ee
\uf0ef
\uf0ed
\uf0ec
\uf0ce\uf03d\uf044\uf03d
\uf03d
\uf02b\uf03d\uf0a2
4,1;6,01,0)(
4)1(
.32
xxhxy
y
yxy
 
X 0,6 0,7 0,8 0,9 1,0 1,1 1,2 1,3 1,4 
Y(x) 
cb XXaY 21 ..\uf03d
 
 
9) Resolver pelo método iterativo de Gauss-Seidel: (\uf078a\uf0a310
-4) 
\uf0ef
\uf0ef
\uf0ef
\uf0ee
\uf0ef\uf0ef
\uf0ef
\uf0ed
\uf0ec
\uf02d\uf03d\uf02d\uf02d\uf02b\uf02b\uf02d
\uf02d\uf03d\uf02d\uf02b\uf02b\uf02b\uf02d
\uf03d\uf02d\uf02b\uf02b\uf02d
\uf02d\uf03d\uf02b\uf02b\uf02d\uf02b
\uf03d\uf02d\uf02d\uf02b\uf02b\uf02d
13517232
14313
131223
86
1428
zwtxy
wtzyx
wtxyz
yzxtw
twzyx
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
10) Calcule um raiz real de:x2- ex= 0 com precisão de 0,000000001.