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Multiple Choice
Use the graph of f(x)to estimate the value of the limit or state that it does not exist (DNE). limx→−2f(x)
A
−3
B
1
C
4
D
DNE
Verified step by step guidance
1
Step 1: Understand the problem. We are tasked with estimating the limit of f(x) as x approaches -2, using the graph provided. A limit exists if the function approaches the same value from both the left and the right sides of the given x-value.
Step 2: Analyze the graph near x = -2. Observe the behavior of the function as x approaches -2 from the left (x → -2⁻) and from the right (x → -2⁺).
Step 3: From the graph, note that as x approaches -2 from the left, the function appears to approach a value near y = 5. However, as x approaches -2 from the right, the function appears to approach a value near y = 1.
Step 4: Since the function approaches different values (y = 5 from the left and y = 1 from the right), the limit does not exist. This is because the left-hand limit and the right-hand limit are not equal.
Step 5: Conclude that the limit of f(x) as x approaches -2 does not exist (DNE).