The correct option is C 1 Let #160; #160; y = lim_x→∞x(e^1/x 1) = lim_x→∞(e^1/x 1)/1/x Put #160; y = 1x⇒ x→∞⇔ y → 0 ∴ y = lim_y → 0e^ ...

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Substitution Method to Remove Indeterminate Form

limx→∞xe1/x-1...

Question

$lim x \to \infty x (e^{1 / x} - 1)$ equals

0

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Solution

The correct option is C $1$
Let $y = lim x \to \infty x (e^{1 / x} - 1) = lim x \to \infty \frac{(e^{1 / x} - 1)}{1 / x}$
Put $y = \frac{1}{x} \Rightarrow x \to \infty \Leftrightarrow y \to 0$
$∴ y = lim y \to 0 \frac{e^{y} - 1}{y} = 1$

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