use the graph to find the following limits and function value. a. lim f(x) x→3⁻ b. lim f(x) x→3⁺ c. lim f(x)…

use the graph to find the following limits and function value. a. lim f(x) x→3⁻ b. lim f(x) x→3⁺ c. lim f(x) x→3 d. f(3) a. find the limit. select the correct choice below and fill in any answer boxes in your choice. a. lim f(x)=1 (type an integer.) x→3⁻ b. the limit does not exist. b. find the limit. select the correct choice below and fill in any answer boxes in your choice. a. lim f(x)= (type an integer.) x→3⁺ b. the limit does not exist.

use the graph to find the following limits and function value. a. lim f(x) x→3⁻ b. lim f(x) x→3⁺ c. lim f(x) x→3 d. f(3) a. find the limit. select the correct choice below and fill in any answer boxes in your choice. a. lim f(x)=1 (type an integer.) x→3⁻ b. the limit does not exist. b. find the limit. select the correct choice below and fill in any answer boxes in your choice. a. lim f(x)= (type an integer.) x→3⁺ b. the limit does not exist.

Answer

Explanation:

Step1: Analyze left - hand limit

As (x) approaches (3) from the left ((x\to3^{-})), we look at the graph and see the (y) - value the function approaches. From the graph, as (x) gets closer and closer to (3) from the left side, (y = 1).

Step2: Analyze right - hand limit

As (x) approaches (3) from the right ((x\to3^{+})), we look at the graph. As (x) gets closer and closer to (3) from the right side, the (y) - value the function approaches is ( - 1).

Step3: Analyze two - sided limit

The two - sided limit (\lim_{x\to3}f(x)) exists if and only if (\lim_{x\to3^{-}}f(x)=\lim_{x\to3^{+}}f(x)). Since (\lim_{x\to3^{-}}f(x) = 1) and (\lim_{x\to3^{+}}f(x)=- 1), (\lim_{x\to3}f(x)) does not exist.

Step4: Analyze function value

To find (f(3)), we look at the value of the function at (x = 3) on the graph. The open - circle at ((3,1)) and ((3, - 1)) means the function is not defined at (x = 3) in the traditional sense. But if we assume the function value is given by the filled - in point (if any), from the graph, we need to check. If there is no filled - in point, we say the function is not defined at (x = 3).

Answer:

a. (\lim_{x\to3^{-}}f(x)=1) b. (\lim_{x\to3^{+}}f(x)= - 1) c. The limit does not exist. d. The function value (f(3)) is not defined (assuming no filled - in point at (x = 3) on the graph).