Q. 61 - Calculus

Question

Calculate each of limits:

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

Step-by-Step Solution

Answer

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

Step 1. Given Information.

The limit is,

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

Step 2. Finding the solution.

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

Inputting $x=1$,

$$\begin{gathered} =\frac{1}{{\sin }^{-1}1} \\ =\frac{1}{{\displaystyle \frac{\mathrm{\pi }}{2}}} \\ =\frac{2}{\mathrm{\pi }} \end{gathered}$$