Q. 60 - Calculus

Question

Calculate each of the limits:

$\underset{x\to 3}{\lim }\frac{\sqrt{x}}{{\tan }^{-1}\sqrt{x}}$

Step-by-Step Solution

Answer

The solution for the limit $\underset{x\to 3}{\lim }\frac{\sqrt{x}}{{\tan }^{-1}\sqrt{x}}$ is, $\frac{3\sqrt{3}}{\mathrm{\pi }}$.

Step 1. Given Information.

The limit is,

$\underset{x\to 3}{\lim }\frac{\sqrt{x}}{{\tan }^{-1}\sqrt{x}}$

Step 2. Finding the solution.

$\underset{x\to 3}{\lim }\frac{\sqrt{x}}{{\tan }^{-1}\sqrt{x}}$

Inputting $x=3$,

$$\begin{gathered} =\frac{\sqrt{3}}{{\tan }^{-1}\left(\sqrt{3}\right)} \\ =\frac{\sqrt{3}}{{\displaystyle \frac{\mathrm{\pi }}{3}}} \\ =\frac{3\sqrt{3}}{\mathrm{\pi }} \end{gathered}$$