$\underset{x→0}{\lim}\begin{Bmatrix}\tan\begin{pmatrix}\frac{π}{4}-x\end{pmatrix}\end{Bmatrix}^{1/x}$ is equal to
Answer & explanation
Correct answer: option 4
Limit = $e^{\underset{x→0}{\lim}\frac{1}{x}\log\begin{Bmatrix}\tan\begin{pmatrix}\frac{π}{4}-x\end{pmatrix}\end{Bmatrix}}=e^{\underset{x→0}{\lim}\frac{\cot\begin{pmatrix}\frac{π}{4}-x\end{pmatrix}.\sec^2\begin{pmatrix}\frac{π}{4}-x\end{pmatrix}.(-1)}{1}}=e^{-2}$