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Exercícios — Regra de L’Hospital
I. Limites que redundam em 
 ou 
 
=? 	( fazendo 
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, derivando o numerador e o denominador, separadamente, temos: 
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= 
= 
=?		( fazendo
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 logo		 
= 
= - 2
Calcule o limite 
= ?	 ( 
 e 
 
 derivando o numerador e o denominador, separadamente, temos:
 e 
; 
 e 
=
 
 
= 
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Calcule o limite 
=? 
��EMBED Unknown e 
 
 derivando o numerador e o denominador, separadamente, temos: 
 = 
 e 
 ( 
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= 
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Calcule o limite
= ? ( 
��EMBED Unknown e 
��EMBED Unknown derivando o numerador e o denominador, separadamente, temos: 
 e 
 
= 
= 
= ?		
��EMBED Unknown= e 
��EMBED Unknown. Derivando o numerador e o denominador, separadamente, temos: 
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=
=
 e 
��EMBED Unknown . Derivando novamente numerador e o denominador, vem: 
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��EMBED Unknown logo 
=
II. Limites que redundam em 
Calcue limite 
= ? ( 
= 
 ( Fazeno 
��EMBED Unknown e 
 
 derivando o numerador e o denominador, separadamente, temos: 
 e 
 
= 
 =
= ? ( 
= 
 e 
 ( 
( derivando o numerador e o denominador, separadamente, temos: 
 ( 
 Logo 
=
=
III. Limites que redundam em 
Calcule o limite 
=?	( 
= 
 ; Fazendo 
 
= 
= 
e 
 ; derivando o numerador e o denominador, separadamente, temos: 
 e 
 
= 
IV. Limites que redundam em 
, 
, 
Calcular o limite 
= ? ( 
= 
��EMBED Unknown 
 
, fazendo 
��EMBED Unknown e 
 ( derivando o numerador e o denominador, separadamente, temos: 
= 
 e 
 Logo 
=
=0 = 
= ln 1( 
=1 
Calcule o limite 
= ? ( 
 
= 
 e 
; Fazendo: 
��EMBED Unknown e 
 
 derivando o numerador e o denominador, separadamente, temos: 
 
= 
 e 
 ( 
= 2 = 
 ou 
 
= 
 Calcule o limite 
= ?
 que é uma indeterminação.
= 
 e 
��EMBED Unknown e derivando o numerador e o denominador, separadamente, temos: 
��EMBED Unknown= 
= 
 e 
 
 = ln 1 ou 
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