Functions Question 11

Question: $ \underset{x\to 0}{\mathop{\lim }}\frac{|x|}{x}= $

[Roorkee 1982; UPSEAT 2001]

Options:

A) 1

B) -1

C) 0

D) Does not exist

Show Answer

Answer:

Correct Answer: D

Solution:

Since $ \underset{x\to 0-}{\mathop{\lim }}\frac{|x|}{x}=-1 $ and $ \underset{x\to 0+}{\mathop{\lim }}\frac{|x|}{x}=1, $ hence limit does not exist.