Evaluate the following limit: _ x 0 e^ x -e^5 x-5 - Vidyadip

Question

Evaluate the following limit:
$\lim\limits_{\text{x}\rightarrow0}\frac{\text{e}^{\text{x}}-\text{e}^5}{\text{x}-5}$

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Answer

$\lim\limits_{\text{x}\rightarrow0}\frac{\text{e}^{\text{x}}-\text{e}^5}{\text{x}-5}$
$=\lim\limits_{\text{x}\rightarrow0}\frac{\text{e}^{5+\text{h}}-\text{e}^5}{\text{h}}$
$=\text{e}^5\lim\limits_{\text{x}\rightarrow0}\frac{\text{e}^{\text{h}}-1}{\text{h}}$
$=\text{e}^5\times1$
$=\text{e}^5$

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