Q43 / 120 · VITEEE 2018 · Mathematics

The value of $\lim _{x \rightarrow 0} \frac{x^{3} \cot x}{1-\cos x}$ is

  • A
    1
  • B
    $-2$
  • Correct answer
    C
    2
  • D
    0

Solution

$\lim _{x \rightarrow 0} \frac{x^{3} \cot x}{1-\cos x}$ $=\lim _{x \rightarrow 0}\left(\frac{x^{3} \cot x}{1-\cos x} \times \frac{1+\cos x}{1+\cos x}\right)$ $=\operatorname{x}_{x \rightarrow 0}\left(\frac{3}{\sin x}\right) \times \lim _{x \rightarrow 0} \cos x \times \lim _{x \rightarrow 0}(1+\cos x)=2$

Hence, the correct answer is option: 'C'.

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