Question

lf $f\left(x\right)=x,x<0;f\left(x\right)=0,x=0$; $f\left(x\right)=x^2;x>0$, then $\underset{x\to 0}{lim}f\left(x\right)$ is equal to

• A. Does not exist
• B. $0$
• C. $-1$
• D. $1$

Answer 1

The correct option is B $0$

Given: $f\left(x\right)$= $\left\{\begin{array}{c}x\\ 0\\ x^2\end{array}\begin{array}{c}x<0\\ x=0\\ x>0\end{array}\right\}$

To Find : $\underset{x\to 0}{lim}$ $f\left(x\right)$= ?

Sol: left hand limit $\to$ $\underset{x\to 0^{-}}{lim}$ $f\left(x\right)$=$\underset{x\to 0}{lim}$ $x$ =$0$

right hand limit $\to$ $\underset{x\to 0^{+}}{lim}$ f(x)=$\underset{x\to 0}{lim}$ $x^2$ =$0$,

LHL=RHL

$f\left(0\right)=0$

$LHL=RHL=f\left(0\right)=0$