First slide

Introduction to limits

Question

The value of $lim_{x \to π / 2} \frac{\cot x - \cos x}{(π - 2 x)^{3}},$ is

Moderate

A

$\frac{1}{2}$
B

$\frac{1}{4}$
C

$\frac{1}{8}$
D

$\frac{1}{16}$

Solution

We have,
$\begin{array}{l} lim_{x \to π / 2} \frac{\cot x - \cos x}{(π - 2 x)^{3}} \\ = lim_{x \to π / 2} \frac{\tan (\frac{π}{2} - x) - \sin (\frac{π}{2} - x)}{8 {(\frac{π}{2} - x)}^{3}} = \frac{1}{8} \times \frac{1}{2} = \frac{1}{16} \end{array}$

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