First slide

Introduction to limits

Question

$lim_{x \to 0^{-}} \frac{\sin x}{\sqrt{x}}$ is equal to

Moderate

A

0
B

1
C

$- \frac{1}{2}$
D

none of these

Solution

We have,
$lim_{x \to 0^{-}} \frac{\sin x}{\sqrt{x}} = lim_{h \to 0} \frac{\sin (- h)}{\sqrt{- h}} = - lim_{h \to 0} \frac{\sin h}{\sqrt{- h}}$
Clearly, $\sqrt{- h}$ is not defined
$∴ lim_{x \to 0^{-}} \frac{\sin x}{\sqrt{x}}$ does not exist in $R$

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