Graphical Limits:
1. For the function \( f \) whose graph is given, state the value of each, if it exists.
![graph_of_a_function](../images/pic.png)
(a) \(\displaystyle{\lim_{x \to -2^+} f(x) } \) (b) \(\displaystyle{\lim_{x \to -2^-} f(x) } \) (c) \(\displaystyle{\lim_{x \to -2} f(x) } \) (d) \(\displaystyle{\lim_{x \to -3} f(x) } \) (e) \(\displaystyle{\lim_{x \to 4^-} f(x) } \) (f) \(\displaystyle{\lim_{x \to 4^+} f(x) } \) (g) \(\displaystyle{\lim_{x \to 4} f(x) } \) (h) \(\displaystyle{\lim_{x \to 2} f(x) } \) (i) \(\displaystyle{f(-3)}\) solution
2. Evaluate the following limits based on the given graph of the function \(f\). If a limit does not exist, state DNE. solution
![](../images/pic2.png)
(a) \(\displaystyle{\lim_{x \to 0} f(x) } \) (b) \(\displaystyle{\lim_{x \to 2^+} f(x) } \) (c) \(\displaystyle{\lim_{x \to 2^-} f(x) } \) (d) \(\displaystyle{\lim_{x \to 2} f(x) } \) (e) \(\displaystyle{\lim_{x \to 3} f(x) } \)
3. Use the graph of the function f to find the following
limits. Solution
(a) \(\displaystyle{\lim_{x \to 2^-} f(x) }\)
(b) \(\displaystyle{\lim_{x \to 2^+} f(x) }\) (c)
\(\displaystyle{\lim_{x \to 2} f(x) }\)
![graph of a function](../images/pic1.gif)