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

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Professor PC Thomas Classes · Answer

(b) : $\lim _{x ightarrow 0} \frac{e^{x^{2}}-\cos x}{\sin ^{2} x}$\ $=\lim _{x ightarrow 0} \frac{2 x e^{x^{2}}+\sin x}{2 \sin x \cos x}$\ (Using L' Hospital's Rule)\ $=\lim _{x ightarrow 0}\left(\frac{x}{\sin x} e^{x^{2}}+\frac{1}{2}ight) \frac{1}{\cos x}=1+\frac{1}{2}=\frac{3}{2}$\