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
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1
Observe the graph of the function f(x). Notice that there is a horizontal line at y = 2 for x < 1 and another horizontal line at y = 2 for x > 1.
Identify the open circle at x = 1 on the graph, which indicates that the function f(x) is not defined at x = 1.
To find the limit as x approaches 1, examine the behavior of the function as x approaches 1 from both the left and the right.
As x approaches 1 from the left (x -> 1^-), the function value approaches 2. Similarly, as x approaches 1 from the right (x -> 1^+), the function value also approaches 2.
Since the function approaches the same value (2) from both sides as x approaches 1, the limit exists and is equal to 2.