_ x 0^ + x e ^ 1 / x 1+ e ^ 1 / x = - Vidyadip

MCQ

$\lim _{x \rightarrow 0^{+}} \frac{x e ^{1 / x}}{1+ e ^{1 / x}}=$

✓
$0$
B
1
C
$\infty$
D
None of these

✓

Answer

Correct option: A.

$0$

(A)
$\lim _{x \rightarrow 0^{+}} \frac{x}{1+ e ^{-1 / x}}-0$ as $e ^{-1 / x} \rightarrow 0$ when $x \rightarrow 0^{+}$

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