2.1 Q-3

Q2. Use the given graph to find each limit $(x\to 1)$, if it exists. (a)

\section*{Solution:}

From graph, it is clear that the limiting value of function approaches to 3 from both left and right side as $x$ approaches to 1 . i.e., ${\lim }_{x\to 1^{-}}f(x)={\lim }_{x\to 1^{+}}f(x)=3$ ⇒ Limit exists. Hence ${\lim }_{x\to 1}f(x)=3$ (b)

\section*{Solution:}

As $x\to 1$ from left, the limiting value of the function approaches to 2 and from the right, it approaches to infinity $(\infty )$. Both limits are not same. Thus, the limit of the function does not exists.

\section*{Evaluate the following:}