use the graph to find the following limits. (a) lim f(x) (b) lim f(x) x→1 x→3 (a) find lim f(x) or state…

use the graph to find the following limits. (a) lim f(x) (b) lim f(x) x→1 x→3 (a) find lim f(x) or state that it does not exist. select the correct choice below and, x→1 if necessary, fill in the answer box within your choice. o a. lim f(x)= (round to the nearest integer as needed.) x→1 o b. the limit does not exist. (b) find lim f(x) or state that it does not exist. select the correct choice below and, x→3 if necessary, fill in the answer box within your choice. o a. lim f(x)= (round to the nearest integer as needed.) x→3 o b. the limit does not exist.

use the graph to find the following limits. (a) lim f(x) (b) lim f(x) x→1 x→3 (a) find lim f(x) or state that it does not exist. select the correct choice below and, x→1 if necessary, fill in the answer box within your choice. o a. lim f(x)= (round to the nearest integer as needed.) x→1 o b. the limit does not exist. (b) find lim f(x) or state that it does not exist. select the correct choice below and, x→3 if necessary, fill in the answer box within your choice. o a. lim f(x)= (round to the nearest integer as needed.) x→3 o b. the limit does not exist.

Answer

Explanation:

Step1: Analyze limit as x→1

As x approaches 1 from both the left - hand side and the right - hand side of the graph, the function values approach the same y - value. Looking at the graph, when x gets closer and closer to 1 (from both directions), the y - value of the function approaches 0. So, $\lim_{x\rightarrow1}f(x)=0$.

Step2: Analyze limit as x→3

As x approaches 3 from the left - hand side, the function values approach a certain y - value, and as x approaches 3 from the right - hand side, the function values approach a different y - value. Since the left - hand limit and the right - hand limit are not equal, $\lim_{x\rightarrow3}f(x)$ does not exist.

Answer:

(a) A. $\lim_{x\rightarrow1}f(x)=0$ (b) B. The limit does not exist.