The GATE Grind

GATE 2023 IN – Question 23

Engineering Mathematics · Calculus and vector calculus · 1 mark · Multiple choice

The limit $\lim_{x\to0}x\sin(1/x)$ is

  1. 0
  2. 1
  3. $\infty$
  4. Limit does not exist

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Show answer and explanation

Correct answer: (A) 0

Explanation

The bound $|x\sin(1/x)|\le|x|$ tends to zero from both sides. The squeeze theorem therefore gives limit **0, A**.