{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

SolsMath262Winter2010

# SolsMath262Winter2010 - Sols Math 262 Winter 2010 1.a f(x =...

This preview shows pages 1–2. Sign up to view the full content.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Sols. Math 262 Winter 2010 1.a f(x) = 1 3 x + = 1 1 1 2 1 5 ( 2) 5 5 x x-- = + +- = ( ) 2 1 2 2 2 1 ... 1 ... 5 5 5 5 n n x x x --- - +-- + = ( ) 2 2 3 1 1 2 ( 2) ( 2) ... 1 ... 5 5 5 5 n n n x x x +---- +-- + b Series converge if 2 1 5 x- < i.e. 2 1 1 5 x-- < < or 3 7 x- < < At end point 3 x = - , series is 1 5 + 1 5 + 1 5 + 1 5 + … which diverges. At 7 x = , series is 1 5- 1 5 + 1 5- 1 5 + … which diverges 2. S(x) = 3 5 2 sin( ) :sin ... 3! 5! x x x t dt x x =- +- ∫ i.e. S(x) = 6 2 ... 3! x t t dt - + ∫ = 3 7 1 4 1 ( 1) ... ... 3 7.3! (4 1)(2 1)! n n x x x n n---- + +-- (Maclaurin series) S(0.1) = 3 7 10 10 ... 3 7.3!--- + 3 3 1 10 10 3 a-- = < . Hence S(0.1) ≈ . If you just take 1 st term 3 10 (0.1) 3 S- ≈ since 7 3 2 10 10 7.3! a-- = < 3. 2 3 2 ( ) , , , 1,2 ,3 d t t t t t t dt =< > = =< > r r v , 2 0,2,6 d dv t v dt dt κ = = < > = + v a T N 3 2 4 2 4 4...
View Full Document

{[ snackBarMessage ]}

### Page1 / 3

SolsMath262Winter2010 - Sols Math 262 Winter 2010 1.a f(x =...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online