decide whether each limit exists. if a limit exists, estimate its value. (a) lim g(x) x→2 (b) lim g(x) x→3…
decide whether each limit exists. if a limit exists, estimate its value. (a) lim g(x) x→2 (b) lim g(x) x→3 (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 g(x)= x→2 b. the limit does not exist. (b) 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 g(x)= x→3 b. the limit does not exist.
Answer
Explanation:
Step1: Analyze limit as x approaches 2
As x approaches 2 from both the left - hand side and the right - hand side of the graph of (y = g(x)), the function values approach the same value. Looking at the graph near (x = 2), the function seems to approach (y=2).
Step2: Analyze limit as x approaches 3
As x approaches 3 from the left - hand side, the function values are approaching a certain value. But as x approaches 3 from the right - hand side, the function values are approaching a different value. So, the left - hand limit and the right - hand limit are not equal at (x = 3).
Answer:
(a) A. (\lim_{x\rightarrow2}g(x)=2) (b) B. The limit does not exist.