To describe: The limit can fail to exist in several ways.
The limit fails to exist for several ways are:
Here approaches to two different values depending on direction of x approaches from. In graph and .
(ii) When the function approach a infinity large value the limit fails to exits.
In the graph doesn’t not exist, because the function has not approach a
(iii) When the function doesn’t approach a particular value then the limit of the function doesn’t exist
Example: as x approaches 0.
The function starts the oscillations faster. The function oscillates between 1 and –1.
(iv) When x-value is approaching the endpoint of a closed interval the limit of the function doesn’t exist.
In the graph the function is only defined for x-values to the right of 0, but x doesn’t approach from the left. So the both sides are not equal then the limit of the function doesn’t exist.
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