What is the value of _ x 0 e^X( ^2x) x^3 ? - Vidyadip

MCQ

What is the value of $\lim_\limits{\text{x} \rightarrow 0}\frac{\text{e}^\text{X}(\sin^2\text{x})}{\text{x}^3}?$

A
$2$
B
$3$
✓
$1$
D
$0$

✓

Answer

Correct option: C.

$1$

$\lim_\limits{\text{x} \rightarrow 0}\frac{\sin^2}{\text{x}^2}\times\lim_\limits{\text{x} \rightarrow 0}\frac{\text{e}^x}{\text{x}}$
We apply L’Hospital’s rule and differentiate numerator and denominator.
$1\times\lim_\limits{\text{x} \rightarrow 0}\frac{\text{e}^x}{\text{1}}$
$= 1$

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