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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→1f(x)
A
0
B
1
C
2
D
DNE
Verified step by step guidance
1
Step 1: Observe the graph of f(x) and identify the behavior of the function as x approaches 1 from both the left and the right.
Step 2: From the graph, note that as x approaches 1 from the left (x → 1⁻), the value of f(x) is approaching 2.
Step 3: Similarly, as x approaches 1 from the right (x → 1⁺), the value of f(x) is also approaching 2.
Step 4: Since the left-hand limit and the right-hand limit are equal, the overall limit exists and is equal to the value that f(x) approaches, which is 2.
Step 5: Conclude that lim_{x→1}f(x) = 2 based on the consistent behavior of the function from both sides of x = 1.