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NDA 2012
Exam
NDA
Year
2012
Subject
Mathematics
Chapter
Limits

NDA 2012 · Mathematics · Limits

What is _ x arrow 0 x^2 ((1)/(x)) equal to?

What is lim⁡x→0x2sin⁡(1x)\lim _{x \rightarrow 0} x^2 \sin \left(\frac{1}{x}\right) equal to?

Options

  1. A0
  2. B1
  3. C1/2
  4. DLimit does not exist

Correct answer

A. 0

Step-by-step solution

lim⁡x→0\lim _{x \rightarrow 0}\left(x^2\right)[sin⁡(1x)]\left[\sin \left(\frac{1}{x}\right)\right] since sin⁡1x\sin \frac{1}{x} is odd and x2x^2 approaches to zero =0=0.
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