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Limits and Derivatives — Maths STD 11 Science — Question

CBSE BoardEnglish MediumSTD 11 ScienceMathsLimits and Derivatives1 Mark
MCQ
$\lim_{x\rightarrow 0} x \sin  \frac{1}{\text{x}}$ is equal to:
  • ✓
    $0$
  • B
    $1$
  • C
    $ \frac{1}{2}$
  • D
    does not exist
✓

Answer

Correct option: A.
$0$
We know that,
$= \lim_\limits{\text{x}\rightarrow 0} \text{x} = 0$
And
$= -1 \leq \sin \frac{1}{\text{x}} \leq 1$
By Sandwich theorem,
$=\lim_\limits{\text{x}\rightarrow 0} \text{x} \sin \frac{1}{\text{x}}$
$=0$

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