JEE Mains · Maths · STD 11 - 12. limits
\(\lim\limits_{x \rightarrow 0}\left(\frac{3 x^{2}+2}{7 x^{2}+2}\right)^{\frac{1}{x^{2}}}\) is equal to
- A \(\frac{1}{e}\)
- B \(e^2\)
- C \(e\)
- D \(\frac{1}{e^2}\)
Answer & Solution
Correct Answer
(D) \(\frac{1}{e^2}\)
Step-by-step Solution
Detailed explanation
Required limit \(=e^{\lim _{x \rightarrow 0}\left(\frac{3 x^{2}+2}{7 x^{2}+2}-1\right) \frac{1}{x^{2}}}\) \(=e^{\lim _{x \rightarrow 0}\left(\frac{-4}{7 x^{2}+2}\right)}=\frac{1}{e^{2}}\)
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