Q100 / 160 · TS EAMCET 2007 · Mathematics

$\lim _{x \rightarrow 0} \frac{e^x-e^{\sin x}}{2(x-\sin x)}$

  • A
    $-1 / 2$
  • Correct answer
    B
    $1 / 2$
  • C
    $1$
  • D
    $3 / 2$

Solution

$\lim _{x \rightarrow 0} \frac{e^x-e^{\sin x}}{2(x-\sin x)}$ $\begin{aligned} & =\lim _{x \rightarrow 0} \frac{e^{\sin x}\left(e^{x-\sin x}-1\right)}{2(x-\sin x)}=\frac{e^0}{2} \times 1 \\ & =\frac{1}{2}\end{aligned}$

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

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