Evaluate the following limit: _ x 0 e^sinx-1 x - Vidyadip

Question

Evaluate the following limit:
$\lim\limits_{\text{x}\rightarrow0}\frac{\text{e}^\text{sinx}-1}{\text{x}}$

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Answer

$\lim\limits_{\text{x}\rightarrow0}\frac{\text{e}^\text{sinx}-1}{\text{x}}$
$=\lim\limits_{\text{x}\rightarrow0}\frac{\text{e}^\text{sinx}-1}{\text{sinx}}\times\lim\limits_{\text{x}\rightarrow0}\frac{\text{sinx}}{\text{x}}$
$=\text{log e}\times1$
$=1$

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