The correct option is C e Let, nbsp; L=lim_x→ 0(1+x)^1/x Taking log both side, ⇒log L=lim_x→ 0log (1+x)x=1 ⇒ L=e ...

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Multinomial Expansion

limx→ 01+x1/x...

Question

$lim x \to 0 (1 + x)^{1 / x}$ equals

1

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0

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e

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\frac{1}{e}

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Solution

The correct option is C $e$
Let, $L = lim x \to 0 (1 + x)^{1 / x}$
Taking $log$ both side,
$\Rightarrow log L = lim x \to 0 \frac{log (1 + x)}{x} = 1$
$\Rightarrow L = e$

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