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