Evaluate the following limit: _ x 0 e^ 3x -e^ 2x x - Vidyadip

Question

Evaluate the following limit:
$\lim\limits_{\text{x}\rightarrow0}\frac{\text{e}^{3\text{x}}-\text{e}^{2\text{x}}}{\text{x}}$

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Answer

$\lim\limits_{\text{x}\rightarrow0}\frac{\text{e}^{3\text{x}}-\text{e}^{2\text{x}}}{\text{x}}$
$=3\lim\limits_{\text{x}\rightarrow0}\frac{\text{e}^{3\text{x}}-1\text{}}{3\text{x}}-\lim\limits_{\text{x}\rightarrow0}\frac{\text{e}^{2\text{x}}-1\text{}}{2\text{x}}$
$=3-2$
$=1$

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