One-sided limit

A one-sided limit is the value a function approaches as its input approaches a point from only one direction, from the left or the right.

Left-hand limit: The value a function approaches as its input approaches a point through smaller inputs. It is the one-sided limit taken from the left.
Piecewise function: A function defined by different formulas on different parts of its domain. Different formulas on either side can produce distinct one-sided limits.
Two-sided limit: A limit that describes a function's behavior as its input approaches a point from both directions. It exists only when the left- and right-hand limits agree.
Open interval: An interval that excludes both of its endpoints. Open intervals provide nearby inputs on either side of interior points.
Right-hand limit: The value a function approaches as its input approaches a point through larger inputs. It is the one-sided limit taken from the right.
Jump discontinuity: A discontinuity where finite left-hand and right-hand limits exist but are unequal. Unequal one-sided limits are the defining signature of a jump.
Function value: The output assigned by a function to a particular input. A one-sided limit need not equal the function's value at the point.
Domain of a function: The set of inputs for which a function is defined. A domain may permit approach from only one side near a boundary.
Epsilon–delta definition of a limit: A formal definition of a function limit using bounds on output and input distances. Its input-distance condition is restricted to one side of the point.
Removable discontinuity: A discontinuity at a point where the finite two-sided limit exists but the function value differs or is undefined. Matching one-sided limits can expose a removable hole.

Linked from 6 pages