Limit of [1 + sin(x)]^(1/x) when x approaches 0

  • Thread starter rene
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Can somebody solve this problem: the limit of [1 + sin(x)]^(1/x) when x approaches 0 ?
 

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Take the logarithm of that expression, which will let you use L'Hopital to solve it.
 
arildno
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The simplest is to rewrite this as:
[tex](1+\sin(x))^{\frac{1}{x}}=((1+\sin(x))^{\frac{1}{\sin(x)}})^{\frac{\sin(x)}{x}}[/tex]
The correct limit is quite easy to deduce from this.
 

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