First slide

Introduction to limits

Question

The value of $lim_{x \to \infty} x \cos (\frac{π}{4 x}) \sin (\frac{π}{4 x}),$ is

Moderate

A

$\frac{π}{2}$
B

$\frac{π}{4}$
C

1
D

none of these

Solution

We have,
$lim_{x \to \infty} \frac{x}{2} \sin (\frac{π}{2 x}) = lim_{x \to \infty} \frac{\sin (\frac{π}{2 x})}{(\frac{π}{2 x})} \cdot \frac{π}{4} = \frac{π}{4} \times 1 = \frac{π}{4}$

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