Use the graph of f(x)to estimate the value of the limit or state that it does not exist (DNE).
A
−1
B
0
C
1
D
DNE
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1
Observe the graph of the function f(x) provided. Notice the behavior of the graph as x approaches 0 from both the left and the right.
Identify the vertical line at x = 0. This line suggests that the function f(x) has a discontinuity at x = 0.
Examine the values of f(x) as x approaches 0 from the left side (x → 0⁻). The graph shows that the values of f(x) are oscillating and do not settle to a single value.
Similarly, examine the values of f(x) as x approaches 0 from the right side (x → 0⁺). The graph again shows oscillation without settling to a single value.
Conclude that since the function does not approach a single value from either side as x approaches 0, the limit limx→0f(x) does not exist (DNE).