How to find the ONE-SIDED LIMITS of a function (KristaKingMath)

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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 right-hand limit at x=a is the value the function approaches as x gets very close to "a" as you move in from the right-hand side (or positive side) of "a". And the left-hand limit at x=a is the value the function approaches as x gets very close to "a" as you move in from the left-hand side (or negative side) of "a".

It's these left- and right-hand limits that we call one-sided limits, and it's important to understand how to calculate one-sided 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 left-hand limit must exist at x=a, the right-hand limit must exist at x=a, and the value of the left- and right-hand 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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