Question

use the graph to find the following limits and function value. a. \\( \lim_{x \to 3^{-}} f(x) \\) b. \\( \lim_{x \to 3^{+}} f(x) \\) c. \\( \lim_{x \to 3} f(x) \\) d. \\( f(3) \\)

Explanation:

Step1: Find left limit at x=3

Check graph as x approaches 3 from left: value approaches -2.

Step2: Find right limit at x=3

Check graph as x approaches 3 from right: value approaches 1.

Step3: Check existence of limit at x=3

Left limit (-2) ≠ right limit (1), so limit does not exist.

Step4: Find function value at x=3

Check graph for closed dot at x=3: value is 1.

Answer:

a. -2
b. 1
c. Does not exist
d. 1