QuestionUse the figure below, which gives a graph of the function $f(x)$, to give values for the indicated limits. If a limit does not exist, enter DNE.
Note: You can click on the graph to enlarge the image. (a) $\lim _{x \rightarrow-2^{-}} f(x)=$ $\square$ help (limits) (b) $\lim _{x \rightarrow-2^{+}} f(x)=$ $\square$ (c) $\lim _{x \rightarrow-2} f(x)=$ $\square$ (d) $\lim _{x \rightarrow-1} f(x)=$ $\square$

Studdy Solution
Identify the limit of $f(x)$ as $x$ approaches $-1$.
From the graph, as $x$ approaches $-1$ from both the left and the right, $f(x)$ approaches -4. The graph is continuous at $x = -1$. Thus, $$\lim_{x \to -1} f(x) = -4$$
Solution: (a) $\lim_{x \to -2^-} f(x) = 0$ \\ (b) $\lim_{x \to -2^+} f(x) = -4$ \\ (c) $\lim_{x \to -2} f(x) = \text{DNE}$ \\ (d) $\lim_{x \to -1} f(x) = -4$