Question

If $f\left(x\right)=\{\begin{array}{cc}1+x,& x>0\\ x,& x<0\end{array},$ then the limiting value of $f\left(x\right)$ when $x\to 0:$

• A. $0$
• B. $\frac{1}{2}$
• C. $1$
• D. does not exist

Answer 1

The correct option is D does not exist

$f\left(x\right)=\{\begin{array}{cc}1+x,& x>0\\ x,& x<0\end{array},$
$L.H.L.=\underset{x\to 0^{-}}{lim}\left(x\right)=0$
$R.H.L.=\underset{x\to 0^{+}}{lim}(1+x)=1+0=1$
Clearly, $L.H.L.\ne R.H.L.$
Hence, limit does not exist.