plugin-Math255-Pset-7 solutions

plugin-Math255-Pset-7 solutions - Winter 2010 Math 255...

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Unformatted text preview: Winter 2010 Math 255 Problem Set 7 Due Tuesday, February 23 Section 15.3: 20, 24, 44, 60, 68, 71, 80 Section 15.4: 4, 24, 38, 42 Section 15.5: 4, 28, 47, 56 Solution and grading suggestion Section 15.3 20. f ( s, t ) = st 2 s 2 + t 2 . f ( s,t ) s = t 2 ( s 2 + t 2 )- st 2 (2 s ) ( s 2 + t 2 ) 2 = t 4- s 2 t 2 ( s 2 + t 2 ) 2 , f ( s,t ) t = 2 st ( s 2 + t 2 )- st 2 (2 t ) ( s 2 + t 2 ) 2 = 2 s 3 t ( s 2 + t 2 ) 2 . 24. f ( x, y ) = R x y cos( t 2 ) dt . f ( x,y ) x = cos( x 2 ), f ( x,y ) y =- cos( y 2 ). 44. sin( xyz ) = x +2 y +3 z with x and y being variables. Take x partial derivative for both sides: cos( xyz ) ( yz + xy z x ) = 1 + 3 z x , So z x = yz cos( xyz )- 1 3- xy cos( xyz ) . Take y partial derivative for both sides: cos( xyz ) xz + xy z y = 2 + 3 z y , So z y = xz cos( xyz )- 2 3- xy cos( xyz ) . 1 Winter 2010 Math 255 60. f ( r, s, t ) = r ln( rs 2 t 3 ) f r = ln( rs 2 t 3 ) + r s 2 t 3 rs 2 t 3 = ln( rs 2 t 3 ) + 1 f rs = 2 rst 3 rs 2 t 3 = 2 s So f rss =- 2 s 2 and f rst = 0....
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This note was uploaded on 12/31/2011 for the course MATH 255 taught by Professor Jackwaddell during the Fall '08 term at University of Michigan.

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plugin-Math255-Pset-7 solutions - Winter 2010 Math 255...

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