Functions Question 680
Question: $ \underset{x\to 1}{\mathop{\lim }},\frac{1}{|1-x|}= $
Options:
A) 0
B) 1
C) 2
D) $ \infty $
Show Answer
Answer:
Correct Answer: D
Solution:
$ \underset{x\to 1-}{\mathop{\lim }},\frac{1}{|1-x|}=\underset{h\to 0}{\mathop{\lim }},\frac{1}{1-(1-h)}=\infty $ and $ \underset{x\to 1+}{\mathop{\lim }},\frac{1}{|1-x|}=\underset{h\to 0}{\mathop{\lim }},\frac{1}{1+h-1}=\infty $ Hence $ \underset{x\to 1}{\mathop{\lim }}\frac{1}{|1-x|}=\infty . $
BETA
