TS EAMCET · Maths · Limits
\(\lim _{x \rightarrow 0} \frac{e^x-e^{\sin x}}{2(x-\sin x)}\)
- A \(-1 / 2\)
- B \(1 / 2\)
- C \(1\)
- D \(3 / 2\)
Answer & Solution
Correct Answer
(B) \(1 / 2\)
Step-by-step Solution
Detailed explanation
\(\lim _{x \rightarrow 0} \frac{e^x-e^{\sin x}}{2(x-\sin x)}\) \(\begin{aligned} & =\lim _{x \rightarrow 0} \frac{e^{\sin x}\left(e^{x-\sin x}-1\right)}{2(x-\sin x)}=\frac{e^0}{2} \times 1 \\ & =\frac{1}{2}\end{aligned}\)
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