Questions: For the following function g(x), determine the value of each limit. If it does not exist, indicate that with DNE. a) lim x -> 2 g(x)= b) lim x -> 0 g(x)= Select the answer choice with the correct answer for parts (a) and (b).

For the following function g(x), determine the value of each limit. If it does not exist, indicate that with DNE.
a) lim x -> 2 g(x)=
b) lim x -> 0 g(x)=
Select the answer choice with the correct answer for parts (a) and (b).

Transcript text: 13) For the following function $g(x)$, determine the value of each limit. If it does not exist, indicate that with DNE. a) $\lim _{x \rightarrow 2} g(x)=$ $\qquad$ b) $\lim _{x \rightarrow 0} g(x)=$ $\qquad$ Select the answer choice with the correct answer for parts (a) and (b).

Solution

Solution Steps

Step 1: Determine the limit as x approaches 2 for g(x)

To find $\lim_{{x \to 2}} g(x)$, observe the behavior of the function $g(x)$ as $x$ approaches 2 from both the left and the right. From the graph, as $x$ approaches 2 from both sides, $g(x)$ approaches 3.

Step 2: Determine the limit as x approaches 0 for g(x)

To find $\lim_{{x \to 0}} g(x)$, observe the behavior of the function $g(x)$ as $x$ approaches 0 from both the left and the right. From the graph, as $x$ approaches 0 from both sides, $g(x)$ approaches -1.

Final Answer

a) $\lim_{{x \to 2}} g(x) = 3$

b) $\lim_{{x \to 0}} g(x) = -1$

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