$-11$ Points$]$

SESSCALCET$21\mathrm{.}3.$AE$\mathrm{.}007.$

$$ EXAMPLE $7$ The graph of a function $g$ is shown in the figure. Use it to state the values $($if they exist$)$ of the following:

$($a$)\underset{x{2}^{-}}{lim}g(x)$

$($b$)\underset{x{2}^{+}}{lim}g(x)$

$($c$)\underset{x2}{lim}g(x)$

$($d$)\underset{x{5}^{-}}{lim}g(x)$

$($e$)\underset{x{5}^{+}}{lim}g(x)$

$($f$)\underset{x5}{lim}g(x).$

SOLUTION From the graph we see that the values of $g(x)$ approach $$ as $x$ approaches $2$ from the left, but they approach $x$ approaches $2$ from the right. Therefore

$($a$)\underset{x{2}^{-}}{lim}g(x)=$ and

$($b$)\underset{x{2}^{+}}{lim}g(x)=$

$($c$)$ Since the left and right limits are different, we conclude that the limit as $x$ approaches $2$ of $g(x)$ does not exist.

The graph also shows that

$($d$)\underset{x{5}^{-}}{lim}g(x)=$

and $(e)\underset{x{5}^{+}}{lim}g(x)=$

$$

$($f$)$ This time, the left and right limits are the same and so$,$ by this theorem, we have

$\underset{x5}{lim}g(x)=$

Need Help? $$ Despite this fact, notice that $g(5)1.$

$$

$5.[1/1$ Points$]$ SESSCALCET$21\mathrm{.}3\mathrm{.}502.$XP$.$