A) \[0\]
B) \[1/2\]
C) \[1\]
D) \[3/2\]
Correct Answer: C
Solution :
\[\underset{x\to 0}{\mathop{\lim }}\,\frac{{{e}^{{{x}^{2}}}}-\cos x}{{{x}^{2}}}\] \[\left[ \frac{0}{0}\,form \right]\] \[=\underset{x\to 0}{\mathop{\lim }}\,\frac{2x{{e}^{{{x}^{2}}}}+sinx}{2x}\] \[\left[ \frac{0}{0}\,form \right]\] \[=\underset{x\to 0}{\mathop{\lim }}\,\,\frac{2{{e}^{{{x}^{2}}}}+4{{x}^{2}}{{e}^{{{x}^{2}}}}+\cos x}{2}\] \[=\frac{2+0+1}{2}=\frac{3}{2}\]
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