First slide

Introduction to limits

Question

The value of $lim_{x \to 0} \frac{| x |}{x},$ is

Moderate

A

1
B

-1
C

0
D

none of these

Solution

We have,
$\begin{array}{l} lim_{x \to 0^{+}} \frac{| x |}{x} = lim_{x \to 0^{+}} \frac{x}{x} = 1 \\ and, lim_{x \to 0^{-}} \frac{| x |}{x} = lim_{x \to 0^{+}} \frac{| - x |}{- x} = lim_{x \to 0^{+}} \frac{x}{- x} = - 1 \end{array}$
Hence, $lim_{x \to 0} \frac{| x |}{x}$ does not exist

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