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GATE2019 CE-2: 3

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The following inequality is true for all $x$ close to $0$.

$$2-\dfrac{x^2}{3} < \dfrac{x \sin x}{1- \cos x} <2$$

What is the value of $\underset{x \to 0}{\lim} \dfrac{x \sin x}{1 – \cos x}$?

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

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