- Definition: A function f is continuous at a number a if
This definition implicitly requires three things if f is continuous at a:
1. f(a) is defined (that is, a is in the domain of f)
- If and are continuous functions with and
, find .
Use the definition of continuity and the properties of limits to show that the funtion is continous at the given number a. ,
- The Intermediate Value Theorem
Suppose that is continuous on the closed interval and let be any number between and , where . Then there exists a number in such that .
~ ~ ~
Use the Intermediate Value Theorem to show that there is
a root of the given equation in the specified interval.