Q43 / 125 · BITSAT 2021 · Mathematics

Value of $\lim _{x \rightarrow 0} \frac{a^{\sin x}-1}{\sin x}$ is

  • Correct answer
    A
    $\log \mathrm{a}$
  • B
    $\sin x$
  • C
    $\log (\sin x)$
  • D
    $\cos x$

Solution

We have, $\lim _{x \rightarrow 0} \frac{a^{\sin x}-1}{\sin x}=\lim _{y \rightarrow 0} \frac{a^{y}-1}{y}$ $=\log \mathrm{a}$, where $\mathrm{y}=\sin \mathrm{x}$ $\because \mathrm{x} \rightarrow 0 \Rightarrow \mathrm{y}=\sin \mathrm{x} \rightarrow 0$

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

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