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Limits — Maths STD 11 Science — Question

Maharashtra BoardEnglish MediumSTD 11 ScienceMathsLimits2 Marks
MCQ
The value of $\lim _{x \rightarrow 0} \frac{ e ^x- e ^{\sin x}}{2(x-\sin x)}$ is
  • A
    $-\frac{1}{2}$
  • ✓
    $\frac{1}{2}$
  • C
    1
  • D
    $\frac{3}{2}$
✓

Answer

Correct option: B.
$\frac{1}{2}$
(B)
$\lim _{x \rightarrow 0} \frac{ e ^x- e ^{\sin x}}{2(x-\sin x)}=\frac{1}{2} \lim _{x \rightarrow 0} e ^{\sin x}\left(\frac{ e ^{x-\sin x}-1}{(x-\sin x)}\right)$
$=\frac{1}{2} \times e ^0 \times 1=\frac{1}{2}$

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