Q. 59 - Calculus

Question

Calculate each of the limits:

$\underset{x\to 1}{\lim }x{\sin }^{-1}\frac{x}{2}$.

Step-by-Step Solution

Answer

The solution for the limit $\underset{x\to 1}{\lim }x{\sin }^{-1}\frac{x}{2}$ is, $\frac{\mathrm{\pi }}{6}$.

Step 1. Given Information.

The limit is,

$\underset{x\to 1}{\lim }x{\sin }^{-1}\frac{x}{2}$.

Step 2. Finding the solution.

$\underset{x\to 1}{\lim }x{\sin }^{-1}\frac{x}{2}$

Inputting $x=1$,

$$\begin{gathered} =1{\sin }^{-1}\left(\frac{1}{2}\right) \\ =1\times \frac{\mathrm{\pi }}{6} \\ =\frac{\mathrm{\pi }}{6} \end{gathered}$$