First slide

Introduction to limits

Question

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

Moderate

A

1
B

-1
C

0
D

none of these

Solution

We have,
$lim_{x \to 0} \frac{\sin x}{\sqrt{x^{2}}} = lim_{x \to 0} \frac{\sin x}{| x |}$
Now $lim_{x \to 0^{-}} \frac{\sin x}{| x |} = lim_{x \to 0} \frac{\sin x}{- x} = - 1$
and $lim_{x \to 0^{+}} \frac{\sin x}{| x |} = lim_{x \to 0} \frac{\sin x}{x} = 1$
Hence $lim_{x \to 0} \frac{\sin x}{| x |}$ dose not exist.

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