Question

If $f\left(x\right)=\{\begin{array}{c}x:x<0\\ 1:x=0\\ x^2:x>0\end{array}$ then $\underset{x\to 0}{lim}f\left(x\right)$ =

• A. 0
• B. 1
• C. 2
• D. does not exist

Answer 1

The correct option is D does not exist

$f\left(x\right)=\{\begin{array}{c}x:x<0\\ 1:x=0\\ x^2:x>0\end{array}$

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

so first find

L.H.L $\underset{x\to 0^{-}}{lim}x=0$

R.H.L $\underset{x\to 0^{+}}{lim}{x}^2=0$

But given

$\underset{x\to 0}{lim}f\left(x\right)=1$

So, we can say that limit

at x = 0 does not exist.