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GATE 2019 CE (CE2) – Question 13

Engineering Mathematics · Calculus: Limits, continuity, mean value theorems, maxima and minima, Taylor series · 1 mark · Multiple choice

For x close to zero, $2-x^2/3<\frac{x\sin x}{1-\cos x}<2$. Find $\lim_{x\to0}\frac{x\sin x}{1-\cos x}$.

  1. 0
  2. 1/2
  3. 1
  4. 2

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Correct answer: (D) 2

Explanation

Both bounds $2-x^2/3$ and 2 tend to 2 as x tends to zero. The squeeze theorem therefore gives the limit **2, D**.