|
|
|
|
Sometimes we may want to find
out if a function is continuous at some value of X.
|
|
|
Usually, we can
just look at the equation or the graph and see. |
|
|
For math types, however,
something being obvious isn't good enough.
|
|
|
They
need formal tests. |
|
|
|
|
|
Two tests must
be passed to say that a function is continuous |
|
|
|
|
|
#1
|
|
|
The value of
the function at the X value we're checking must be a real
number. |
|
|
Not something
like infinity, or the square root of negative five, or undefined. |
|
|
|
|
|
#2 |
|
|
The limit of the function at
our X value must exist
|
|
|
and be equal to the value of the function at that X value.
|
|
|
|
|
|
If we call the value of X that
we are interest in "c",
|
|
|
then we can write these tests as the
questions:
|
|
|
|
|
|
| 1 |
Does
F(c) = some real number? |
|
|
| 2 |
Does |
Lim
F(X) |
=
that same real number? |
| X
®
c |
|
|
|
|
|
|
If we can
answer yes to both questions, then the function is continuous at
that X value. |
|
|
|
|
|
copyright 2005 Bruce
Kirkpatrick |
|