Question

$\underset{x\to 0}{\lim }{\left(\frac{3x^2+2}{7x^2+2}\right)}^{1/x^2}$ is equal to :

• A. $e$
• B. $\frac{1}{e^2}$
• C. $\frac{1}{e}$
• D. $e^2$

Answer 1

Answer: (B)

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