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NDA 2022
Exam
NDA
Year
2022
Subject
Mathematics
Chapter
Limits

NDA 2022 · Mathematics · Limits

What is _ x arrow 0 x^3(cosec x)^2 equal to?

What is lim⁡x→0x3(cosec⁡x)2\lim _{x \rightarrow 0} x^3(\operatorname{cosec} x)^2 equal to?

Options

  1. A0
  2. B12\frac{1}{2}
  3. C1
  4. DLimit does not exist

Correct answer

A. 0

Step-by-step solution

lim⁡x→0x3(cosec⁡x)2=lim⁡x→0x3sin⁡2x=lim⁡x→0(xsin⁡x)2⋅x=1.0=0\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}
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