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

x→1
a. lim g(x) 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)=1 as x→2
b. lim g(x) does not exist as x→2

c. what is lim g(x) as x→3? choose the correct answer below and, if necessary, fill in the answer box to complete your choice.
a. lim g(x)=□ as x→3
b. lim g(x) does not exist as x→3

Explanation:

Step1: Analyze limit as x→1

As x approaches 1 from the left - hand side and the right - hand side, the function values do not approach the same value. So, $\lim_{x
ightarrow1}g(x)$ does not exist.

Step2: Analyze limit as x→2

As x approaches 2 from both the left - hand side and the right - hand side, the function values approach 1. So, $\lim_{x
ightarrow2}g(x)=1$.

Step3: Analyze limit as x→3

As x approaches 3 from the left - hand side and the right - hand side, the function values do not approach the same value. So, $\lim_{x
ightarrow3}g(x)$ does not exist.

Step4: Analyze limit as x→2.5

As x approaches 2.5 from both the left - hand side and the right - hand side, the function values approach a well - defined value. But since the problem does not ask for this limit, we focus on the given ones.

Answer:

a. B. $\lim_{x
ightarrow1}g(x)$ does not exist
b. A. $\lim_{x
ightarrow2}g(x)=1$
c. B. $\lim_{x
ightarrow3}g(x)$ does not exist