limx→0 x sin 1 x is equal to: - Vidyadip

MCQ

lim_x→0 x sin $ \frac{1}{\text{x}}$ is equal to:

A
0
B
1
C
$ \frac{1}{2}$
D
does not exist

✓

Answer

0

Solution:

We know that,

$= \lim_\limits{\text{x}→0} \text{x} = 0$

And

$= -1 ≤ \sin \frac{1}{\text{x}} ≤ 1$

By Sandwich theorem,

$$ $=\lim_\limits{\text{x}→0} \text{x} \sin \frac{1}{\text{x}} =0$

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