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Question: Answered & Verified by Expert
$\lim _{x \rightarrow 0} \frac{e^x-e^{\sin x}}{2(x-\sin x)}$
MathematicsLimitsTS EAMCETTS EAMCET 2007
Options:
  • A $-1 / 2$
  • B $1 / 2$
  • C $1$
  • D $3 / 2$
Solution:
2628 Upvotes Verified Answer
The correct answer is: $1 / 2$
$\lim _{x \rightarrow 0} \frac{e^x-e^{\sin x}}{2(x-\sin x)}$
$\begin{aligned} & =\lim _{x \rightarrow 0} \frac{e^{\sin x}\left(e^{x-\sin x}-1\right)}{2(x-\sin x)}=\frac{e^0}{2} \times 1 \\ & =\frac{1}{2}\end{aligned}$

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