puc Segunda Prova de Calculo Numerico 2018
1 pág.

puc Segunda Prova de Calculo Numerico 2018

Disciplina:Cálculo Numérico11.508 materiais244.301 seguidores
Pré-visualização1 página
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.