Maharashtra BoardEnglish MediumSTD 11 ScienceMathsLimits2 Marks
MCQ
$\lim _{x \rightarrow 0} \frac{ e ^x+ e ^{-x}-2}{x^2}=$
✓
1
B
-1
C
$\frac{1}{2}$
D
$-\frac{1}{2}$
✓
Answer
Correct option: A.
1
(A) $\lim _{x \rightarrow 0} \frac{ e ^x+ e ^{-x}-2}{x^2}=\lim _{x \rightarrow 0} \frac{ e ^x+\frac{1}{ e ^x}-2}{x^2}$ $=\lim _{x \rightarrow 0} \frac{\left( e ^x\right)^2-2 e ^x+1}{x^2 e ^x}=\lim _{x \rightarrow 0}\left(\frac{ e ^x-1}{x}\right)^2 \cdot \frac{1}{ e ^x}$ $=(1)^2 \cdot \frac{1}{ e ^0}=1$
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