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Multiple Choice
Find the limit using the graph of f(x)shown. limx→−2f(x)
A
4
B
−2
C
−3
D
Unable to determine
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Verified step by step guidance
1
Step 1: Understand the problem. The goal is to find the limit of f(x) as x approaches -2 using the graph provided. A limit describes the value that f(x) approaches as x gets closer to a specific point.
Step 2: Analyze the graph near x = -2. Observe the behavior of the function f(x) as x approaches -2 from both the left-hand side (x → -2⁻) and the right-hand side (x → -2⁺).
Step 3: From the graph, note that as x approaches -2 from the left, the function f(x) approaches -3. Similarly, as x approaches -2 from the right, the function f(x) also approaches -3.
Step 4: Confirm that the left-hand limit and right-hand limit are equal. Since both limits are -3, the overall limit exists and is equal to -3.
Step 5: Conclude that lim_{x→-2}f(x) = -3 based on the graph's behavior near x = -2.