Math 104 Rimmer
8.7 Approximate
Integration
b
Goal: To approximate
f ( x ) dx.
a
Why? a ) You can't find the antiderivative of f ( x ) .
b ) You don't have a formula for f ( x ) .
i ) You have a graph only
ii ) You have a table of values
We already know
Math 104 Rimmer
10.3 Integral Test
If f ( x ) is: a ) continuous, on the interval
b ) positive,
c ) and decreasing
,then the series
a ( with a
n
n
[ k , )
constant k > 0
= f ( n)
n =k
i ) is convergent when
f ( x ) dx is convergent.
k
ii ) is divergent
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Math 104 Rimmer
9.1 Intro to Diff. Eq.
9.1 Introduction to Differential Eq.
A differential equation is an equation that involves a derivative
As soon as you learned how to find the anti-derivative, you were solving your first
differential equation.
This i
Math 104 Rimmer
10.1 Sequences
10.1 Sequences
A sequence is an ordered list of numbers.
A sequence can be finite or infinite.
countably many
numbers in the list
In this class we will deal
with infinite sequences
infinitely many
numbers in the list
Note: t
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Math 104 Rimmer
8.8 Improper Integrals
An integral can be called improper with one or any combination of the following:
Examples:
e
Infinite upper limit
2 x
e
dx = lim
t
1
8
1
t
= lim
dx
x
= lim+
dx
2 x 4
= lim
0
9
lower limit
0
some value between