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Limits — Maths STD 11 Science — Question

Maharashtra BoardEnglish MediumSTD 11 ScienceMathsLimits2 Marks
MCQ
$\lim _{x \rightarrow 0} \frac{e^{\frac{1}{x}}}{e^{\left(\frac{1}{x}+1\right)}}=$
  • A
    $0$
  • B
    1
  • C
    does not exist
  • ✓
    $e ^{-1}$
✓

Answer

Correct option: D.
$e ^{-1}$
(D)
$\lim _{x \rightarrow 0} \frac{ e ^{1 / x}}{ e ^{\left(\frac{1}{x}+1\right)}}=\lim _{x \rightarrow 0} \frac{ e ^{1 / x}}{ e ^{\frac{1}{x}} \cdot e }=\lim _{x \rightarrow 0} \frac{1}{ e }= e ^{-1}$

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