



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 
