Chapter 1: Q. 58 (page 136)

Calculate each of the limits:
$\lim_{x \to \frac{π}{2}} \frac{c o t x}{\cos x}$ .

Short Answer

Expert verified

The solution for the limit $\lim_{x \to \frac{π}{2}} \frac{c o t x}{\cos x}$ is, $1$ .

Step by step solution

Step 1. Given Information.

The limit is,

$\lim_{x \to \frac{π}{2}} \frac{c o t x}{\cos x}$ .

Step 2. Finding the solution.

$\lim_{x \to \frac{π}{2}} \frac{c o t x}{\cos x}$

Inputting $c o t x = \frac{\cos x}{\sin x}$ ,

role="math" localid="1647974061831" $= \lim_{x \to \frac{π}{2}} \frac{\frac{\cos x}{\sin x}}{\cos x} = \lim_{x \to \frac{π}{2}} \frac{\cos x}{\sin x \times \cos x} = \lim_{x \to \frac{π}{2}} \frac{1}{\sin x} = \frac{1}{\sin \frac{π}{2}} = \frac{1}{1} = 1$

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Calculate each of the limits:
$\lim_{x \to \frac{π}{2}} \frac{c o t x}{\cos x}$ .

Short Answer

Step by step solution

Step 1. Given Information.

Step 2. Finding the solution.

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Short Answer

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Calculate each of the limits:
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