Calculus

Definition

is continuous at

This also implicitly requires that:

  1. is defined
  2. exists

A function is continuous on an interval it is continuous at every number in that interval. Continuity has sidedness. A function can be continuous from the left or right if the limit is one sided.


Laws of Continuity

  1. If and are continuous at then the following are continuous at .
  2. is continuous at and is continuous at is continuous at
  3. is continuous at and

Continuous Functions

Polynomials, Rational, Root and Trigonometric Functions are all continuous for all numbers in their domain.


Intermediate Value Theorem

is continuous on and


Extreme Value Theorem

is continuous on attains a global maximum and minimum value on