Since given function is of form 00 , so using L'Hopital's rule: lim #160; _ x → 0e^x 1 sinx = lim #160; _ x → 0e^x cosx=e^0cos0=1 ...

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Substitution Method to Remove Indeterminate Form

limit x → 0...

Question

$l i m i t_{x \to 0} \frac{e^{x} - 1}{s i n x}$

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Solution

Since given function is of form $\frac{0}{0}$ , so using L'Hopital's rule:
$l i m_{x \to 0} \frac{e^{x} - 1}{s i n x}$ = $l i m_{x \to 0} \frac{e^{x}}{c o s x} = \frac{e^{0}}{c o s 0} = 1$

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