Limits Continuity And Differentiability Question 35
Question: Which of the following function(s) has/have removable discontinuity at $ x=1 $ ?
Options:
A) $ f(x)=\frac{1}{In| x |} $
B) $ f(x)=\frac{1}{x^{3}-1} $
C) $ f(x)={2^{{2^{\frac{1}{1-x}}}}} $
D) $ f(x)=\frac{\sqrt{x+1}-\sqrt{2x}}{x^{2}-x} $
Show Answer
Answer:
Correct Answer: D
$ \underset{x\to 1}{\mathop{\lim }}f(x) $ does not exist. [b] $ \underset{x\to 1}{\mathop{\lim }}f(x)= $ does not exist. [c] $ \underset{x\to 1}{\mathop{\lim }}f(x) $ does not exist. [d] $ \underset{x\to 1}{\mathop{\lim }}f(x)=\frac{-1}{2\sqrt{2}}, $ therefore $ f(x) $ has removable discontinuity at $ x=1 $ .
BETA
