Question

use the graph to determine the limit. (if an answer does not exist, enter dne.) (a) $lim_{x
ightarrow c^{+}}f(x)=$ (b) $lim_{x
ightarrow c^{-}}f(x)=$ (c) $lim_{x
ightarrow c}f(x)=$ is the function continuous at $x = 1$? yes no

Explanation:

Step1: Right-hand limit as x→1⁺

From graph, x→1⁺ approaches (1,-3). $\lim_{x \to 1^+} f(x) = -3$

Step2: Left-hand limit as x→1⁻

From graph, x→1⁻ approaches (1,3). $\lim_{x \to 1^-} f(x) = 3$

Step3: Overall limit as x→1

Left limit (3) ≠ Right limit (-3). $\lim_{x \to 1} f(x) = \text{DNE}$

Step4: Continuity at x=1

Limit DNE, so not continuous.

Answer:

(a) -3
(b) 3
(c) DNE
No