Power Series / Final

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17 Terms

1
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Power Series for 1/1-r

r^n

2
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Geo Series Convergence

r < 1

3
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IOC for r=0

-inf, inf

4
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IOC for r=inf

0

5
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Ratio and Root test convergence

L < 1

6
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Power series for ln(1-x)

x^n/n

7
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Taylor/Mac series of e^x

x^n/n!

8
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IOC for Taylor/Mac series of e^x

-inf, inf

9
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Definition of a Maclaurin Series

series [(f^(nth ‘)(0)/n!]*(x^n)

10
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Definition of a Taylor Series

series [f^(nth ‘)(a)/n!]*(x-a)^n

11
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How to check endpoints for convergence?

Substitute back into series; use convergence test

12
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cosh x function

(e^x + e^-x)/2

13
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sinh x function

(e^x - e^-x)/2

14
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Second derivative

[d/dt(dy/dx)]/(dx/dt)

15
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X and Y for polar eq’s

x = r cos, y = r sin

16
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2sin x cos x

sin(2x)

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AST

-1)^(n) a(n), decreasing, lim a(n) = 0