Question

decide whether each limit exists. if a limit exists, estimate its value. (a) $lim_{x
ightarrow1}g(x)$ (b) $lim_{x
ightarrow2}g(x)$ (a) what is the value of the limit? select the correct choice below and, if necessary, fill in the answer box within your selection. a. $lim_{x
ightarrow1}g(x)=square$ b. the limit does not exist.

Explanation:

Step1: Analyze left - hand limit as x→1

As x approaches 1 from the left, g(x) approaches 2.

Step2: Analyze right - hand limit as x→1

As x approaches 1 from the right, g(x) approaches 2.
Since the left - hand limit and the right - hand limit are equal as x→1, the limit exists.

Step3: Analyze left - hand limit as x→2

As x approaches 2 from the left, g(x) approaches 3.

Step4: Analyze right - hand limit as x→2

As x approaches 2 from the right, g(x) approaches 1.
Since the left - hand limit and the right - hand limit are not equal as x→2, the limit does not exist.

Answer:

(a) A. $\lim_{x
ightarrow1}g(x)=2$
(b) B. The limit does not exist.