The value of $\underset{x→0}{\lim}(1+x^2+\sin x)^{3/\tan x}$ is equal to
Answer & explanation
Correct answer: option 4
$\underset{x→0}{\lim}(1+x^2+\sin x)^{3/\tan x}=\underset{x→0}{\lim}(1+x^2+\sin x)^{\frac{1}{x^2+\sin x}×\frac{3(x^2+\sin x)}{\tan x}}=e^{3\underset{x→0}{\lim}\frac{x^2+\sin x}{\tan x}}=e^3$