Question

determine whether each limit exists. if a limit exists, estimate its value.
(a) $lim_{x
ightarrow - 3}f(x)$
(b) $lim_{x
ightarrow0}f(x)$
(a) find the one - sided limits.
$lim_{x
ightarrow - 3^{-}}f(x)=square$
$lim_{x
ightarrow - 3^{+}}f(x)=square$

Explanation:

Step1: Analyze left - hand limit as $x\to - 3$

As $x$ approaches $-3$ from the left side ($x\to - 3^{-}$), we look at the values of $y = f(x)$ on the graph for $x$ values slightly less than $-3$. By observing the graph, we can estimate the value.

Step2: Analyze right - hand limit as $x\to - 3$

As $x$ approaches $-3$ from the right side ($x\to - 3^{+}$), we look at the values of $y = f(x)$ on the graph for $x$ values slightly greater than $-3$. By observing the graph, we can estimate the value.

Answer:

(a) $\lim_{x\to - 3^{-}}f(x)$: [Estimated value from the graph for left - hand approach to $x=-3$]
$\lim_{x\to - 3^{+}}f(x)$: [Estimated value from the graph for right - hand approach to $x = - 3$]
(b) To find $\lim_{x\to0}f(x)$, we would follow similar steps of finding one - sided limits as $x\to0^{-}$ and $x\to0^{+}$ by observing the graph for values of $y = f(x)$ as $x$ approaches $0$ from the left and right respectively. But since the question only asks for part (a) one - sided limits for now, we focus on the above answers for part (a).