Calculus II Power Series Introduction by: javier section 151.05.01

Calculus II Power Series Introduction

π =4−

4 4 4 + − + ··· 3 5 7

by: javier section 151.05.01

Understanding the Power in Power Series

The Key Idea

Understanding the Power in Power Series

functions

sin(x)

polynomials

−1 + 3x + 5x2 arctan(x)

1 √ 1− x

The two worlds

x + 12 x − 13 x3 1 − x + x2 − x3

Understanding the Power in Power Series

functions

sin(x)

polynomials

−1 + 3x + 5x2 arctan(x)

1 √ 1− x

The two worlds

x + 12 x − 13 x3 1 − x + x2 − x3

Understanding the Power in Power Series

functions

sin(x)

polynomials

−1 + 3x + 5x2 arctan(x)

1 √ 1− x

The two worlds

x + 12 x − 13 x3 1 − x + x2 − x3

Understanding the Power in Power Series

functions

sin(x)

polynomials

−1 + 3x + 5x2 arctan(x)

1 √ 1− x

The two worlds

x + 12 x − 13 x3 1 − x + x2 − x3

Understanding the Power in Power Series

functions

sin(x)

polynomials

−1 + 3x + 5x2 arctan(x)

1 √ 1− x

The two worlds

x + 12 x − 13 x3 1 − x + x2 − x3

Understanding the Power in Power Series

functions

sin(x)

polynomials

−1 + 3x + 5x2 arctan(x)

1 √ 1− x

The two worlds

x + 12 x − 13 x3 1 − x + x2 − x3

Understanding the Power in Power Series

functions

sin(x)

polynomials

−1 + 3x + 5x2 arctan(x)

1 √ 1− x

The two worlds

x + 12 x − 13 x3 1 − x + x2 − x3

Understanding the Power in Power Series

functions

sin(x)

polynomials

−1 + 3x + 5x2 arctan(x)

1 √ 1− x

The two worlds

x + 12 x − 13 x3 1 − x + x2 − x3

Understanding the Power in Power Series

functions

sin(x)

polynomials

−1 + 3x + 5x2 arctan(x)

1 √ 1− x

The two worlds

x + 12 x − 13 x3 1 − x + x2 − x3

Examples using CCT

Examples using CCT

example: it

1 1−x

xtxtxstx

'tX5tX 't

'

itxtxtxt

#×

.

xtitxk

it

=

.+×%5± X

what if x=t

we

.

+×*

substitute

-

or

tt+=

×=

I

-

-

-

.+xa=g÷= Ex

.

.

.

1×1