Question

for the function g(x) graphed here, find the following limits or state that they do not exist.
a. lim g(x) as x→1 b. lim g(x) as x→2 c. lim g(x) as x→3 d. lim g(x) as x→2.5
a. what is lim g(x) as x→1? choose the correct answer below and, if necessary, fill in the answer box to complete your choice.
a. lim g(x) as x→1 =
b. lim g(x) as x→1 does not exist
b. what is lim g(x) as x→2? choose the correct answer below and, if necessary, fill in the answer box to complete your choice.
a. lim g(x) as x→2 =
b. lim g(x) as x→2 does not exist

Explanation:

Step1: Analyze limit as $x\to1$

As $x$ approaches 1 from the left and right, the function values do not approach the same value. The left - hand limit and right - hand limit are different. So, $\lim_{x\to1}g(x)$ does not exist.

Step2: Analyze limit as $x\to2$

As $x$ approaches 2 from the left, the function value approaches 1. As $x$ approaches 2 from the right, the function value also approaches 1. So, $\lim_{x\to2}g(x)=1$.

Answer:

a. B. $\lim_{x\to1}g(x)$ does not exist
b. A. $\lim_{x\to2}g(x)=1$