Question

decide from the graph whether each limit exists. if a limit exists, estimate its value. (a) \\( \lim _{x \
ightarrow-6} f(x) \\) (b) \\( \lim _{x \
ightarrow-8} 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 \
ightarrow-6} f(x)=-4 \\) (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 \
ightarrow-8} f(x)= \\) (round to the nearest integer as needed.) b. the limit does not exist.

Explanation:

Step1: Analyze the limit as \(x\to - 6\)

When finding \(\lim_{x
ightarrow - 6}F(x)\), we look at the behavior of the function \(y = F(x)\) as \(x\) approaches \(-6\). From the graph, as \(x\) gets closer and closer to \(-6\) (from both the left - hand side and the right - hand side), the \(y\) - value approaches \(-4\).

Step2: Analyze the limit as \(x\to - 8\)

When finding \(\lim_{x
ightarrow - 8}F(x)\), we check the behavior of the function as \(x\) approaches \(-8\). If we look at the graph, as \(x\) approaches \(-8\) from the left - hand side and the right - hand side, the function \(y = F(x)\) does not approach a single finite value.

Answer:

(a) A. \(\lim_{x
ightarrow - 6}F(x)=-4\)
(b) B. The limit does not exist.