SolsMath262Winter2010

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

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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 = = < > = + v a T N 3 2 4 2 4 4...
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This note was uploaded on 12/21/2010 for the course MATH 262 taught by Professor Faber during the Spring '08 term at McGill.

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

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