L=lim_x→ 0(x+1)^1/x log L=1xlog (x+1) log L=log (x+1)x L Hopital rule, log L=1x+1=1 L=e^1=e ...

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Factorization Method Form to Remove Indeterminate Form

limx→ 0x+11/x...

Question

$lim x \to 0 (x + 1)^{\frac{1}{x}}$ .

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Solution

$L = {lim}_{x \to 0} {(x + 1)}^{\frac{1}{x}}$
$log L = \frac{1}{x} log (x + 1)$
$log L = \frac{log (x + 1)}{x}$
$L - H o p i t a l$ rule,
$log L = \frac{1}{x + 1} = 1$
$L = e^{1} = e$

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