2 pág.

# lista-civil-13.pdf

DisciplinaCálculo I77.465 materiais1.370.280 seguidores
Pré-visualização1 página
```CURSO: ENGENHARIA CIVIL \u2013 2013.2
TURMAS: 2MA / 2MB / 2NA / 2NB
DISCIPLINA: CÁLCULO DIFERENCIAL E INTEGRAL I
ALUNO (a)_____________________________________________________________________________________
PROFESSOR: Esp. Miguel Aquino de Lacerda Neto
\u2022LISTA DE EXERCÍCIOS\u2022
1. Calcular o valor de \ufffd em cada situação pedida, usando a definição de limite.
a)lim\ufffd\u2192\ufffd
3\ufffd
2\ufffd \ufffd
5 , \ufffd\ufffd\ufffd\ufffd \ufffd \ufffd 0,02 b)lim\ufffd\u2192
3\ufffd \ufffd 2\ufffd \ufffd 5, \ufffd\ufffd\ufffd\ufffd \ufffd \ufffd 0,01

c) lim\ufffd\u2192\ufffd\ufffd
5
2\ufffd\ufffd \ufffd 9 , \ufffd\ufffd\ufffd\ufffd \ufffd \ufffd 0,001 d) lim\ufffd\u2192\ufffd	 \ufffd\ufffd\ufffd\ufffd	\ufffd\ufffd	 \ufffd \ufffd
2 , \ufffd\ufffd\ufffd\ufffd \ufffd \ufffd 0,01

e) lim\ufffd\u2192\ufffd
4\ufffd \ufffd 2\ufffd \ufffd
2 , \ufffd\ufffd\ufffd\ufffd \ufffd \ufffd 0,002 f) lim\ufffd\u2192\ufffd
3\ufffd \ufffd 7\ufffd , \ufffd\ufffd\ufffd\ufffd \ufffd \ufffd 0,5

g) lim\ufffd\u2192	 \ufffd\ufffd\ufffd\ufffd	\ufffd\ufffd	 \ufffd \ufffd
2 , \ufffd\ufffd\ufffd\ufffd \ufffd \ufffd 0,75 h) lim\ufffd\u2192\ufffd
2\ufffd \ufffd 4\ufffd \ufffd 8 , \ufffd\ufffd\ufffd\ufffd \ufffd \ufffd 0,01

i) lim\ufffd\u2192&quot; 	\ufffd\ufffd\ufffd \ufffd
# , \ufffd\ufffd\ufffd\ufffd \ufffd \ufffd 0,25 j) lim\ufffd\u2192\ufffd\ufffd \ufffd\ufffd
\ufffd\ufffd\$
\ufffd%\ufffd \ufffd \ufffd
4 , \ufffd\ufffd\ufffd\ufffd \ufffd \ufffd 0,1

2. Usando os limites dados no item anterior, represente graficamente.

3. Demonstre, usando a definição de limite: \u2200 \ufffd ' 0, \u2203 \ufffd ' 0, )* )+,*-.* )*, 0 / |\ufffd
\ufffd| / \ufffd tal que,|1
\ufffd\ufffd
2| / \ufffd ,

a)lim\ufffd\u2192#
4\ufffd
1\ufffd \ufffd 11

b) lim\ufffd\u2192\ufffd \ufffd\ufffd\ufffd\$\ufffd\ufffd\ufffd \ufffd 4

c) lim\ufffd\u2192\ufffd
3\ufffd
2\ufffd \ufffd 4

d) ) lim\ufffd\u2192
\ufffd
2\ufffd \ufffd
1

e)lim\ufffd\u2192&quot; \ufffd\ufffd\ufffd\ufffd&quot;\ufffd\ufffd&quot; \ufffd 10

4. Observando o gráfico a seguir, mostre que o lim\ufffd\u2192#
4\ufffd
5\ufffd \ufffd 7 existe e calcule o valor para \ufffd, sa-bendo que \ufffd \ufffd 0,001,
usando a definição de limite.

5. Calcular os limites a seguir, usando as propriedades justificando cada passagem:
a)lim\ufffd\u21923
3
7\ufffd \ufffd 5\ufffd\ufffd\ufffd b)lim\ufffd\u2192\ufffd
\ufffd&quot; \ufffd 6\ufffd5 \ufffd 2\ufffd c)lim\ufffd\u2192\ufffd	6
\ufffd \ufffd 4\ufffd# \u2219
\ufffd \ufffd 2\ufffd\ufffd	8

d) lim\ufffd\u21929\ufffd62 )*-\ufffd
cos \ufffd \ufffd =+.> \ufffd8 e) lim\ufffd\u2192\ufffd?@
2\ufffd \ufffd 3\ufffd
/\$ f) lim\ufffd\u2192\ufffd \ufffd\ufffd\ufffd%&quot;\ufffd%5\ufffd%\ufffd \ufffd

g)lim\u2192	 \u221a\ufffd\ufffd\ufffd&quot;\ufffd%\$\ufffd@%C\ufffd\ufffd\ufffd h)lim\ufffd\u2192\ufffd# D\ufffd\ufffd
@\ufffd#\ufffd\ufffd%&quot;\ufffd\ufffd	\ufffd
\ufffd\ufffd%\$\ufffd\ufffd	 i)lim\ufffd\u2192\ufffd\ufffd D\ufffd
\ufffd\ufffd&quot;\ufffd%C
\ufffd\ufffd%\ufffd\ufffd\ufffdE
@

6.Mostrar que:

a)Se 1 é a função polinomial, então lim\ufffd\u2192F 1
\ufffd\ufffd \ufffd 1
\ufffd\ufffd para todo o real a.

b)Se g é uma função racional e a pertence ao domínio de g, então lim\ufffd\u2192F >
\ufffd\ufffd \ufffd >
\ufffd\ufffd.

7.Calcule lim\ufffd\u21923 H
\ufffd%I\ufffd\ufffdH