X 0 x 1 x is equals to - Vidyadip

MCQ

$\underset{{X \rightarrow 0}}{\lim} x \sin \frac{1}{x}$ is equals to

A
1
B
does not exist
C
$1 / 2$
D
$0$

✓

Answer

(d) 0
Explanation: $\lim _{z \rightarrow 0} x=0$ and $-1 \leq \sin \frac{1}{z} \leq 1$, by Sandwitch Theorem, we have
$\underset{{z \rightarrow 0}}{\lim} x \sin \frac{1}{z}=0$

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