- Definition: A function f is continuous at a number a if
p>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)
2.
exists
3.
- 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 thatis 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.



