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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