Exercícios Limites

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Matemática para Engenharia I
LISTA 03 - LIMITES
1) Para a f(x) dada, expresse cada um dos seguintes limites: 
, 
 e 
.
a) 
, 
		b) 
, 
 c) 
, 
 (R.: 
, 
, não existe)	 (R.: 
, 
, não existe) (R.: 
, 
, 
)
d) 
, 
 e) 
, 
 (R.: 
, 
, 
)		 (R.: 
, 
, não existe)
2) Determine o limite se existir:
		b) 
		c) 
	
(R.: 1/2)			 R.: 3/2)				 (R.: 0)
d) 
			e) 
			f) 
 (R.: 
)			 (R.: 
)			 (R.: 16)
 g) 
			h) 
			i) 
	
 (R.: não existe)		 (R.: 0)			 	 (R.: 1) 
 j) 
		
 (R.: 0)			 
3) Ache as assíntotas verticais e horizontais do gráfico de f.
 a) 
			b) 
		c) 
 d) 
			e) 
4) Uma função f satisfaz as condições indicadas. Esboce um gráfico de f, supondo que ele não corte uma assíntota horizontal.
 a) 
	
	 b) 
	
 
	
		 
	
								 
	
5) Calcule os limites aplicando os limites fundamentais:
a) 
		 b) 
		c)
		 d) 
		
 (R.: 1)			(R.: 2)			 (R.: 4/3)			 (R.: 3/5)
	
e) 
	 f) 
, 
	g) 
	 h) 
 
 (R.: 3)			(R.: a/b)		 (R.: 2/7)			 (R.: 1/8)
i) 
 	 j) 
 k) 
	 l) 
	
 (R.: 0)			(R.: 
)		 (R.: 
)		 (R.: 
)
m) 
	 n) 
	o) 
	 p) 
 (R.: e)			(R.: 
)		 (R.: 
)			 (R.: 2)
q) 
	 r) 
		s) 
	 t) 
 (R.: 2/3)			(R.: 1)		 (R.: 2)			 (R.: 5/2)
u) 
 v) 
 x)
 y) 
 (R.: 
)		 (R.: e)		 (R.: 
)			 (R.: 
)
z) 
 (R.: 
)
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