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