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Limits — Maths STD 11 Science — Question

Maharashtra BoardEnglish MediumSTD 11 ScienceMathsLimits2 Marks
MCQ
$\lim _{x \rightarrow 0} \frac{\left(1-e^x\right) \sin x}{x^2+x^3}$ is equal to
  • ✓
    -1
  • B
    $0$
  • C
    1
  • D
    2
✓

Answer

Correct option: A.
-1
(A)
$\lim _{x \rightarrow 0} \frac{\left(1- e ^x\right) \sin x}{x^2+x^3}$
$=-\lim _{x \rightarrow 0}\left(\frac{ e ^x-1}{x}\right) \times\left(\frac{\sin x}{x}\right) \times \frac{1}{1+x}$
$=-1 \times 1 \times 1=-1$

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