some function g is graphed below. fill in the blanks in the following sentences.\nas x gets closer and…
some function g is graphed below. fill in the blanks in the following sentences.\nas x gets closer and closer to (but stays less than) 1, g(x) gets as close as we want to 3.\nas x gets closer and closer to (but stays greater than) 1, g(x) gets as close as we want to 2.\nas x gets closer and closer (but not equal) to 1, does g(x) get as close as we want to a single value? if such a value exists, enter it. if no such value exists, enter dne.
Answer
Explanation:
Step1: Analyze left - hand limit
As (x) approaches (1) from the left ( (x<1)), by observing the graph, the (y) - values of the function (g(x)) approach (3).
Step2: Analyze right - hand limit
As (x) approaches (1) from the right ((x > 1)), by observing the graph, the (y) - values of the function (g(x)) approach (2).
Step3: Determine overall limit
For the limit of (g(x)) as (x) approaches (1) to exist, the left - hand limit and the right - hand limit must be equal. Since (\lim_{x\to1^{-}}g(x)=3) and (\lim_{x\to1^{+}}g(x)=2), and (3\neq2), the limit of (g(x)) as (x) approaches (1) does not exist.
Answer:
DNE