Use the graph of in the figure to find the following values or state that they do not exist. If a limit does not exist, explain why. <IMAGE>
limx→2g(x)
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1
Examine the graph of g(x) around x = 2 to understand the behavior of the function as x approaches 2 from both the left and the right.
Identify the left-hand limit, , by observing the values that g(x) approaches as x approaches 2 from the left side.
Identify the right-hand limit, , by observing the values that g(x) approaches as x approaches 2 from the right side.
Compare the left-hand limit and the right-hand limit. If both limits are equal, then the limit exists and is equal to this common value.
If the left-hand limit and the right-hand limit are not equal, then the limit does not exist, and you should explain that the discrepancy between the two limits is the reason for the non-existence.
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