Q224 / 270 · NDA 2022 (Phase 1) · Mathematics

What is $\lim _{x \rightarrow 0} x^3(\operatorname{cosec} x)^2$ equal to?

  • Correct answer
    A
    0
  • B
    $\frac{1}{2}$
  • C
    1
  • D
    Limit does not exist

Solution

$\begin{aligned} & \lim _{x \rightarrow 0} x^3(\operatorname{cosec} x)^2 \\ & =\lim _{x \rightarrow 0} \frac{x^3}{\sin ^2 x}=\lim _{x \rightarrow 0}\left(\frac{x}{\sin x}\right)^2 \cdot x \\ & =1.0=0\end{aligned}$

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

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