9.10 more power series. example 2 problem 6 find the a power series for the function centered at c
Post on 27-Dec-2015
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____4____
5+3 – (x+3) Geometric series with
___4___ first term ½ and r = (x+3)/8
8 – (x+3)
__1/2___
1 – (x+3) ½ + 1/2 (x+3)/8 + 1/2 ((x+3)/8)2 +…
8
We want the form
Problem 10 solution
___-3____ Geometric series with
1 – 2x a= 1 r= -2/3(x -2)
___-3____
1- 4 – 2(x -2)
___-3____
-3 –2(x -2)
___ 1____
1 - 2/3(x -2)
We want the form
If we have a known power series what operations can I use to create a new series?
You may do any of the following
1. replace x by kx (on both sides of the equation)
2. replace x by xn (on both sides of the equation)
3. Add two known series
4. Take the derivative of a known series
5. Find a definite integral from 0 to x of a known series
The Series for
Sinx = x - x3 + x5 - x7… 3! 5! 7!
If we replace x by x-3 on both side will we still get a true equation?
The Series for
Sinx = x - x3 + x5 - x7… 3! 5! 7!
If we replace x by x-3 on both side will we still get a true equation?
No, the left side would equal to sinx shifted 3 the right but the left side would not.
Note: to create other series with non zero centers such as
y= sinx centered at π/2
Use the Taylor series to create the series
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