consider the function g graphed below. g(x)={x + 1, for x<2; -1/2x + 2, for x≥2} find lim g(x). x→2⁻ select…

consider the function g graphed below. g(x)={x + 1, for x<2; -1/2x + 2, for x≥2} find lim g(x). x→2⁻ select the correct choice below and fill in any answer boxes in your choice. a. lim g(x)=□ (type an integer or a simplified fraction.) b. the limit does not exist.

consider the function g graphed below. g(x)={x + 1, for x<2; -1/2x + 2, for x≥2} find lim g(x). x→2⁻ select the correct choice below and fill in any answer boxes in your choice. a. lim g(x)=□ (type an integer or a simplified fraction.) b. the limit does not exist.

Answer

Explanation:

Step1: Identify the function for x < 2

The function for (x<2) is (g(x)=x + 1).

Step2: Calculate the left - hand limit

To find (\lim_{x\rightarrow2^{-}}g(x)), we use the function (g(x)=x + 1) (since we are approaching 2 from the left, (x<2)). Substitute (x = 2) into (g(x)=x + 1). So, (\lim_{x\rightarrow2^{-}}g(x)=2 + 1).

Step3: Simplify the result

(2+1=3).

Answer:

A. (\lim_{x\rightarrow2^{-}}g(x)=3)