Q120 / 170 · Manipal (MET) 2021 · Mathematics

$\lim _{x \rightarrow 0} \frac{\sin 3 x-\sin x}{\sin x}$ is

  • A
    -2
  • Correct answer
    B
    2
  • C
    0
  • D
    None of these

Solution

$\begin{aligned} \lim _{x \rightarrow 0} & \frac{\sin 3 x-\sin x}{\sin x} \\ & =\lim _{x \rightarrow 0} \frac{2 \cos 2 x \sin x}{\sin x}=2\end{aligned}$

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

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