Question

If $f\left(x\right)=\{\begin{array}{cc}4x,& x<0\\ 1,& x=0\\ 3x^2,& x>0\end{array}$ then $\underset{x\to 0}{lim}f\left(x\right)$ equals

• A. 0
• B. 1
• C. 3
• D. does not exist

Answer 1

Answer: (A)

0

Left hand limit, $L^{-}=\underset{x\to 0^{-}}{lim}f\left(x\right)=4.\left(0\right)=0$
and Right hand limit, $L^{+}=\underset{x\to 0^{+}}{lim}f\left(x\right)=3.(0{)}^2=0$
Hence Required limit is $=\underset{x\to 0}{lim}f\left(x\right)=L^{+}=L^{-}=0$