First slide

Introduction to limits

Question

The value of $lim_{x \to 0} \frac{x^{2} \sin (\frac{1}{x})}{\sin x}$ , is

Moderate

A

1
B

0
C

$1 / 2$
D

none of these

Solution

$lim_{x \to 0} \frac{x^{2} \sin (\frac{1}{x})}{\sin x} = lim_{x \to 0} \frac{x}{\sin x} \times x \sin (\frac{1}{x})$
$= 1 \times 0 \times$ (An oscillating number) $= 0$

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