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When the limit as the function approaches from the left, doesn't equal the limit as the function approaches from the right.
For example, let's look at the function 1/x as x approaches 0.
As it approaches 0 from the left, it travels towards negative infinity.
As it approaches 0 from the right, it travels towards positive infinity.
Therefore, the limit of the function as it approaches 0 does not exist.
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