First slide

Introduction to limits

Question

The value of $lim_{x \to 1} (1 - x) \tan (\frac{π x}{2})$ , is

Moderate

A

$π / 2$
B

$π + 2$
C

$2 / π$
D

none of these

Solution

We have,
$\begin{array}{l} lim_{x \to 1} (1 - x) \tan (\frac{π x}{2}) = lim_{x \to 1} (1 - x) \cot (\frac{π}{2} - \frac{π}{2} x) \\ = \frac{2}{π} lim_{x \to 1} \frac{\frac{π}{2} (1 - x)}{\tan \frac{π}{2} (1 - x)} = \frac{2}{π} \times 1 = \frac{2}{π} \end{array}$

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