Question

decide from the graph whether each limit exists. if a limit exists, estimate its value.
(a) $lim_{x
ightarrow3}f(x)$
(b) $lim_{x
ightarrow5}f(x)$
(a) what is the value of the limit? select the correct choice below and, if necessary, fill in the answer box within your choice.
a. $lim_{x
ightarrow3}f(x)=square$ (round to the nearest integer as needed.)
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 choice.
a. $lim_{x
ightarrow5}f(x)=square$ (round to the nearest integer as needed.)
b. the limit does not exist.

Explanation:

Step1: Analyze limit as x→3

Look at the graph near x = 3. As x approaches 3 from both the left - hand and right - hand sides, the y - values of the function F(x) approach 4. So, $\lim_{x
ightarrow3}F(x)=4$.

Step2: Analyze limit as x→5

Look at the graph near x = 5. As x approaches 5 from the left - hand side, the y - values are around 2, and as x approaches 5 from the right - hand side, the y - values are around 2. So, $\lim_{x
ightarrow5}F(x)=2$.

Answer:

(a) $\lim_{x
ightarrow3}F(x)=4$
(b) $\lim_{x
ightarrow5}F(x)=2$