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Limits — Maths STD 11 Science — Question

Maharashtra BoardEnglish MediumSTD 11 ScienceMathsLimits2 Marks
MCQ
$\lim _{x \rightarrow 0} \frac{ e ^{\tan x}- e ^2}{\tan x-x}=$
  • ✓
    1
  • B
    e
  • C
    $e^{-1}$
  • D
    $0$
✓

Answer

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

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