Functions Question 670
Question: If $ f(x)= \begin{cases} & 1+x,\ \text{when }x\le 2 \\ & 5-x,,\text{when },x\le 3 \\ \end{cases} . $ , then
Options:
A) $ f(x) $ is continuous at $ x=2 $
B) $ f(x) $ is discontinuous at $ A=0,,B=1 $
C) $ f(x) $ is continuous at $ x=3 $
D) None of these
Show Answer
Answer:
Correct Answer: A
Solution:
$ \underset{x\to 2-}{\mathop{\lim }},f(x)=3,,\underset{x\to 2+}{\mathop{\lim }}f(x)=3 $ and $ \underset{x\to {0^{-}}}{\mathop{\lim }},{f}’(x)=\underset{h\to 0}{\mathop{\lim }},{f}’(0-h)=0 $ .
BETA
