Calculus: Limits

The limit of the function f(x) as x approaches the point x_o equals the real number L.

The limit of the function f(x) as x approaches the point x_o from the left (as x increases) equals the real number L.

The limit of the function f(x) as x approaches the point x_o from the right (as x decreases) equals the real number L.

An infinite limit approaches infinity as the independent variable x approaches the point x_o.

If f(x_o) equals a real number, then the limit as x approaches x_o is simply f(x_o).

If two functions equal each other at x_o, then the limits of the two functions equal each other as x approaches x_o provided both limits exist.

A function is continuous at x_o if the limit as x approaches x_o equals a real value.

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