Q32Multiple correct5 Marks6 Aug 2023

Define a function $f(x)=\begin{cases}\frac{x-3}{|x-3|}, & x\ne3,\\ 1, & x=3.\end{cases}$ Which of the following options is/are true?

A

$\lim_{x\to3^+}f(x)=f(3)$.

B

$\lim_{x\to3^-}f(x)$ does not exist.

C

$f$ is not continuous at $x=3$.

D

$f$ is differentiable at $x=3$.

E

$f'(3)=1$.