Questions: Use the graph of y=g(x) to determine the following limits. (Use DNE for "does not exist" when applicable. You can click on a graph to enlarge it.) 2. lim x -> 1- g(x)= b. lim x -> 1+ g(x)= c. lim x -> 1 g(x)=

Use the graph of y=g(x) to determine the following limits. (Use DNE for "does not exist" when applicable. You can click on a graph to enlarge it.) 2. lim x -> 1- g(x)= b. lim x -> 1+ g(x)= c. lim x -> 1 g(x)=
Transcript text: Use the graph of $y=g(x)$ to determine the following limits. (Use DNE for "does not exist" when applicable. You can click on a graph to enlarge it.) 2. $\lim _{x \rightarrow 1^{-}} g(x)=$ $\square$ b. $\lim _{x \rightarrow 1^{+}} g(x)=$ $\square$ c. $\lim _{x \rightarrow 1} g(x)=$ $\square$
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Solution

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Solution Steps

Step 1: Analyze the graph as x approaches 1 from the left.

We want to find the limit of \(g(x)\) as \(x\) approaches 1 from the left, denoted as \(\lim_{x \rightarrow 1^{-}} g(x)\). Observe the graph to see the value \(g(x)\) approaches as \(x\) gets closer and closer to 1 from values smaller than 1. Following the curve from the left, we see it approaches the y-value of 2.

Step 2: Analyze the graph as x approaches 1 from the right.

Now we want to find the limit of \(g(x)\) as \(x\) approaches 1 from the right, denoted as \(\lim_{x \rightarrow 1^{+}} g(x)\). Observe the graph to see the value \(g(x)\) approaches as \(x\) gets closer and closer to 1 from values larger than 1. Following the curve from the right, we see it approaches the y-value of 2.

Step 3: Analyze the limit as x approaches 1.

Since \(\lim_{x \rightarrow 1^{-}} g(x) = 2\) and \(\lim_{x \rightarrow 1^{+}} g(x) = 2\), and they are equal, the limit as \(x\) approaches 1 is 2. That is, \(\lim_{x \rightarrow 1} g(x) = 2\).

Final Answer

a. \(\boxed{2}\) b. \(\boxed{2}\) c. \(\boxed{2}\)

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