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The general limit of a function at x=a is the value the function approaches as x gets very close to "a" from either side of "a".

Similarly, the righthand limit at x=a is the value the function approaches as x gets very close to "a" as you move in from the righthand side (or positive side) of "a". And the lefthand limit at x=a is the value the function approaches as x gets very close to "a" as you move in from the lefthand side (or negative side) of "a".

It's these left and righthand limits that we call onesided limits, and it's important to understand how to calculate onesided limits because they're part of the definition of the general limit.

In order for the general limit of a function to exist at x=a, the lefthand limit must exist at x=a, the righthand limit must exist at x=a, and the value of the left and righthand limits must be equal to each other. If all three of these conditions are met, then we can say that the general limit exists at x=a. Otherwise, if any one or more of the conditions are not met, the general limit cannot exist at x=a. If the general limit does not exist, it implies that there's a discontinuity in the graph at that point.

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