Functions Question 111
Question: $ \underset{x\to 2}{\mathop{\lim }},\frac{|x-2|}{x-2}= $
[AI CBSE 1985]
Options:
A) 1
B) ?1
C) Does not exist
D) None of these
Show Answer
Answer:
Correct Answer: C
Solution:
$ \underset{x\to 2-}{\mathop{\lim }},\frac{|x-2|}{x-2}=\underset{h\to 0}{\mathop{\lim }}\frac{|2-h-2|}{2-h-2}=-1 $ and $ \underset{x\to 2+}{\mathop{\lim }},\frac{|x-2|}{x-2}=\underset{h\to 0}{\mathop{\lim }}\frac{|2+h-2|}{2+h-2}=1 $ Hence limit does not exist.
BETA
