Graphical Limits:

1. For the function \( f \) whose graph is given, state the value of each, if it exists.

(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

(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)   \(\displaystyle{\lim_{x \to 2} f(x) }\)