Chapter 11 Review (Test 2) Flashcards Preview

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Flashcards in Chapter 11 Review (Test 2) Deck (11):
1

Ratio Test for Absolute Convergence

p = lim of k approaches infinity of absolute value of a sub k +1 divided by a sub k
If p > 1 , converges for x=0
If p < 1, converges for all x
If p involves x, converges for (a-R, a+R)

2

P-Series Test

If p>1, then converges, alternating converges
If 0 < p less than or equal to 1 then diverges, alternating converges

3

Taylor/Maclaurin Polynomials

sigma of k = 0 to infinity of f to the k derivative of a over k factorial times (x-a) to the k

4

Maclaurin series
E to the x
and E to the -x

1 + x + (x^2)/2! + (x^3)/3! +....
1 - x + (x^2)/2! - (x^3)/3! +....

5

Maclaurin series
sinx

x - (x^3/3!) + (x^5/5!) - ...

6

Maclaurin series
cosx

1 - (x^2)/2! + (x^4)/4! - ...

7

Maclaurin series

1 / 1-x
1 / 1+ x

1 + x + x^2 + x^3 + ...

1 - x + x^2 - x^3

8

Maclaurin series
ln(1+x)

x - (x^2/2) + (x^3)/3 - ...

9

Maclaurin series
inverse tan

x - (x^3/3) + (x^5/5) - ....

10

Error

If alternating, convergent series,

absolute value of error is less than or equal to absolute value of next term

11

Langrange's Form of Remainder

If not alternating and convergent;
Absolute value of R sub n of x is less than or equal to the absolute value of M over (n+1)! times (x-a)to the n+!

M = max value of f to the n+1 of x