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
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1
Identify the point on the graph where x approaches -2. Look at the behavior of the graph as it gets close to x = -2 from both the left and the right.
Observe the left-hand limit as x approaches -2. Follow the graph from the left side towards x = -2 and note the y-value it approaches.
Observe the right-hand limit as x approaches -2. Follow the graph from the right side towards x = -2 and note the y-value it approaches.
Compare the left-hand and right-hand limits. If they approach the same y-value, the limit exists and is equal to that y-value. If they approach different y-values, the limit does not exist.
In this graph, as x approaches -2 from the left, the graph approaches a different y-value than it does from the right, indicating that the limit does not exist (DNE).