A) e
B) \[\frac{1}{e}\]
C) \[\frac{1}{{{e}^{2}}}\]
D) \[{{e}^{2}}\]
Correct Answer: C
Solution :
[c] \[\underset{x\to 0}{\mathop{\lim }}\,{{\left( \frac{3{{x}^{2}}+2}{7{{x}^{2}}+2} \right)}^{\frac{1}{{{x}^{2}}}}}\] \[\Rightarrow {{e}^{\underset{x\to 0}{\mathop{\lim }}\,}}\left( \frac{3{{x}^{2}}+2-7{{x}^{2}}-2}{7{{x}^{2}}+2} \right)\frac{1}{{{x}^{2}}}\] \[\Rightarrow {{e}^{\frac{-4}{3}}}={{e}^{-2}}\]
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