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  4. displaystyle limx → 0 ((3x2+2/7x2+2))1/x2 is equal to :

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Q. $\displaystyle\lim_{x \to 0} \left(\frac{3x^{2}+2}{7x^{2}+2}\right)^{1/x^2}$ is equal to :

JEE MainJEE Main 2020Limits and Derivatives

Solution:

Required limit $=e^{\displaystyle \lim_{x \to 0}\left(\frac{3x^{2}+2}{7x^{2}+2}-1\right) \frac{1}{x^{2}} }$
$=e^{\displaystyle \lim_{x \to 0}\left(\frac{-4}{7x^{2}+2}\right)}$$=\frac{1}{e^{2}}$