Limits of combined functions: piecewise functions | AP Calculus AB | Khan Academy

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Even when the limits of two functions at some point do not exist, the limit of their sum or product might still exist.

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[pythagorasguy]

In the first example, if we find the limits of the functions f(x) and g(x) individually, the one-sided limits aren't equal, so when the limits don't exist how can the limit of their sum be equal to 4?

[mulberrytree]

I'm first I'm first Mr. Khan!