91Ó°ÊÓ

Consider the given information,

Let's take an example to show this statement. The example of a function f and a value c such that $\underset{x→c}{\lim }f\left(x\right)$ happen to be equal to $f\left(c\right)$.

Thatrole="math" localid="1654675695968" $\underset{x→2}{\lim }4=4$.

Here, for role="math" localid="1654675708563" $x→2^{-}$, the value of the function is role="math" localid="1654675722002" $f\left(2^{-}\right)=4$.

And again, for role="math" localid="1654675735716" $x→2^{+}$, the value of the function is role="math" localid="1654675748367" $f\left(2^{+}\right)=4$.

Thus, the example is role="math" localid="1654677607262" $\underset{x→2}{\lim }4=4$.

Consider the example.

$\underset{x→1}{\lim }2x$

Take the left limit of the function.

$\begin{array}{rcl}\underset{x→1^{-}}{\lim }2x& =& 2(0.999)\\ & =& 1.998\end{array}$

Take the right limit of the function.

$\begin{array}{rcl}\underset{x→1^{+}}{\lim }\left(2x\right)& =& 2\left(1.0001\right)\\ & =& 2.0002\end{array}$

Consider the given information,

Let's take an example to explain the statement. $\underset{x→1}{\lim }\frac{1}{x-1}$.

In this case, the limit does not exist if we take the left and right limits.