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Question

$\lim_{x \to 0} \frac{e^{x^{2}} - \cos x}{\sin^{2} x} is equal to$

Smart Achievers · Accepted Answer

(2)

$\lim_{x \to 0} \frac{e^{x^{2}} - \cos x}{\sin^{2} x} = \lim_{x \to 0} \frac{2 x e^{x^{2}} + \sin x}{2 \sin x \cos x}$

$(Using L'Hospital Rule)$

$\lim_{x \to 0} (\frac{x}{\sin x} e^{x^{2}} + \frac{1}{2}) \frac{1}{\cos x} = 1 + \frac{1}{2} = \frac{3}{2}$

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