Question

Discuss the continuity of the function $f$ given by $f\left(x\right)=\left|x\right|$ at $x=0$.

Answer 1

The function is very well continuous at $x=0$

From graph we can see from both side the function approaches $0$

Though the function is not differential at the given point as its a sharp end and $LHD=-1$ and $RHD=1$ thus $LHD$ is not equal to $RHD$.