Question

The graph of the function $y=f\left(x\right)$ is shown in the above figure, then correct statement is -

• A. $\underset{x\to 0^{+}}{lim}f\left(x\right)=1$
• B. $\underset{x\to 1}{lim}f\left(x\right)=2$
• C. $\underset{x\to 3}{lim}f\left(x\right)$ does not not exist
• D. $\underset{x\to 4}{lim}f\left(x\right)=0$

Answer 1

Answer: (A), (B), (C), (D)

The correct options are
A $\underset{x\to 0^{+}}{lim}f\left(x\right)=1$
B $\underset{x\to 1}{lim}f\left(x\right)=2$
C $\underset{x\to 3}{lim}f\left(x\right)$ does not not exist
D $\underset{x\to 4}{lim}f\left(x\right)=0$

$\because$ Limit exists only if $\underset{x\to a^{+}}{lim}f\left(x\right)=\underset{x\to a^{-}}{lim}f\left(x\right)i.e$ LHL=RHL

From graph we can see that,

For option (A), $\underset{x\to 0^{+}}{lim}f\left(x\right)=f\left(0^{+}\right)=1$

For option (B), $\underset{x\to 1}{lim}f\left(x\right)=f\left(1^{-}\right)=f\left(1^{+}\right)=2$

For option (C), $\underset{x\to 3^{-}}{lim}f\left(x\right)=+\infty \ne \underset{x\to 3^{+}}{lim}f\left(x\right)=-\infty$

Hence$\underset{x\to 3}{lim}f\left(x\right)$ does not exist

For option (D), $\underset{x\to 4}{lim}f\left(x\right)=f\left(4\right)=0$

Thus all options are correct