Calculus Limit Test Calculus
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On and On
Limit Test Calculus

 
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

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