Question

$Iff\left(x\right)=\{\begin{array}{cc}\frac{3x-x^2}{2}& x<2\\ [x-1],& 2\le x<3\\ x^2-8x+17,& x\ge 3\end{array}$

then which of the following hold(s) good?

[Note ; [x] denotes largest integer less than or equal to x,]

• A. $\underset{x\to 2}{lim}f\left(x\right)=1$
• B. f(x) is differentiable at x = 2.
• C. f(x) is continuous at x =2
• D. f(x) is discontinuous at x = 3.

Answer 1

Answer: (A), (C), (D)

The correct options are
A

$\underset{x\to 2}{lim}f\left(x\right)=1$

C

f(x) is continuous at x =2

D

f(x) is discontinuous at x = 3.