Limits Continuity And Differentiability Question 58
Question: If the function $ f(x)=\frac{x(x-2)}{x^{2}-4},x\ne \pm 2 $ is continuous at $ x=2 $ , then what is $ f(2) $ equal to?
Options:
A) 0
B) $ \frac{1}{2} $
C) 1
D) 2
Show Answer
Answer:
Correct Answer: B
Solution:
Let $ f(x)=\frac{x(x-2)}{x^{2}-4}=\frac{x(x-2)}{(x-2)(x+2)}=\frac{x}{x+2} $
Since f(x) is continuous at x = 2
$ \therefore \underset{x\to 2}{\mathop{\lim }}f(x)=f(2) $
$ \Rightarrow \underset{x\to 2}{\mathop{\lim }}\frac{x}{x+2}=f(2)\Rightarrow f(2)=\frac{2}{4}=\frac{1}{2} $
BETA
