lista-civil-13.pdf
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" 	\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 , 
cada limite a seguir. 
 
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" \ufffd\ufffd\ufffd\ufffd"\ufffd\ufffd" \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" \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%"\ufffd%5\ufffd%\ufffd \ufffd 
 
g)lim\u2192	 \u221a\ufffd\ufffd\ufffd"\ufffd%$\ufffd@%C\ufffd\ufffd\ufffd h)lim\ufffd\u2192\ufffd# D\ufffd\ufffd
@\ufffd#\ufffd\ufffd%"\ufffd\ufffd	\ufffd
\ufffd\ufffd%$\ufffd\ufffd	 i)lim\ufffd\u2192\ufffd\ufffd D\ufffd
\ufffd\ufffd"\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
\ufffd\ufffdI sendo 1 dada por: 
 
a)1
\ufffd\ufffd \ufffd \ufffd\ufffd b) 1
\ufffd\ufffd \ufffd 2\ufffd\ufffd \ufffd \ufffd c) 1
\ufffd\ufffd \ufffd 5 d) 1
\ufffd\ufffd \ufffd 
\ufffd# \ufffd 2\ufffd e) 1
\ufffd\ufffd \ufffd 	\ufffd f) 1
\ufffd\ufffd \ufffd 3\ufffd \ufffd 1