Q. 26 - Calculus

Question

Find the limit by hand.

$\underset{x\to \infty }{\lim }\sin \left({\tan }^{-1}x\right)$

Step-by-Step Solution

Answer

On solving the limit, we get, $1$.

Step 1. Given information.

Consider the given question,

$\underset{x\to \infty }{\lim }\sin \left({\tan }^{-1}x\right)$

Step 2. Solve the given limit.

Using the limits,

$$\begin{gathered} =\sin \left({\tan }^{-1}\infty \right) \\ =\sin \left(\frac{\mathrm{\pi }}{2}\right) \\ =1 \end{gathered}$$