Questions: Use the graph of f(x) shown below to determine each of the following limits. If any of the limits do not exist, enter ∅ as your answer. Provide your answer below: a. lim x → 2- f(x)= □ b. lim x → 2+ f(x)= □ c. lim x → 2 f(x)= □

Use the graph of f(x) shown below to determine each of the following limits. If any of the limits do not exist, enter ∅ as your answer. Provide your answer below: a. lim x → 2- f(x)= □ b. lim x → 2+ f(x)= □ c. lim x → 2 f(x)= □
Transcript text: Use the graph of $f(x)$ shown below to determine each of the following limits. If any of the limits do not exist, enter $\varnothing$ as your answer. Provide your answer below: a. $\lim _{x \rightarrow 2^{-}} f(x)=$ $\square$ b. $\lim _{x \rightarrow 2^{+}} f(x)=$ $\square$ c. $\lim _{x \rightarrow 2} f(x)=$ $\square$
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Solution

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Solution Steps

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

Observe the graph of f(x) as x approaches 2 from the left (x → 2⁻). The function values approach 3.

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

Observe the graph of f(x) as x approaches 2 from the right (x → 2⁺). The function values approach 3.

Step 3: Determine the limit as x approaches 2.

Since the left-hand limit and the right-hand limit are both equal to 3, the limit as x approaches 2 exists and is equal to 3.

Final Answer

a. $\lim _{x \rightarrow 2^{-}} f(x)=3$ b. $\lim _{x \rightarrow 2^{+}} f(x)=3$ c. $\lim _{x \rightarrow 2} f(x)=3$

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