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Chapter 1: Q. 60 (page 136)

Calculate each of the limits:
$\lim_{x \to 3} \frac{\sqrt{x}}{\tan^{- 1} \sqrt{x}}$

Short Answer

Expert verified

The solution for the limit $\lim_{x \to 3} \frac{\sqrt{x}}{\tan^{- 1} \sqrt{x}}$ is, $\frac{3 \sqrt{3}}{π}$ .

Step by step solution

01

Step 1. Given Information.

The limit is,

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

02

Step 2. Finding the solution.

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

Inputting $x = 3$ ,

$= \frac{\sqrt{3}}{\tan^{- 1} (\sqrt{3})} = \frac{\sqrt{3}}{\frac{π}{3}} = \frac{3 \sqrt{3}}{π}$

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Explain why the Intermediate Value Theorem allows us to say that a function can change sign only at discontinuities and zeroes.

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See all solutions

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