ma100_hw4

ma100_hw4 - Homework answer 4 Sec 13.3 24 r(t) = cos3 ti +...

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Homework answer 4 Sec 13.3 24 ~ r ( t ) = cos 3 t ~ i + sin 3 t ~ j, for 0 6 t 6 π 2 ~ r ( t ) dt = - 3 cos 2 t sin t ~ i + 3 sin 2 t cos t ~ j k ~ r ( t ) dt k = p 9 cos 4 t sin 2 t + 9 sin 4 t cos 2 t = 3 cos t sin t s ( t ) = Z t 0 3 cos l sin l dl = Z t 0 3 sin l d (sin l ) = 3 sin 2 t 2 t ( s ) = arcsin r 2 s 3 , for 0 6 s 6 3 2 ~ r ( s ) = cos 3 (arcsin r 2 s 3 ) ~ i + sin 3 (arcsin r 2 s 3 ) ~ j, for 0 6 s 6 3 2 or = ( 3 - 2 s 3 ) 3 2 ~ i + ( 2 s 3 ) 3 2 ~ j, for 0 6 s 6 3 2 32. dx dt = dr dt cos θ + r sin θ dt dy dt = dr dt sin θ - r cos θ dt L = Z b a r ( dx dt ) 2 + ( dy dt ) 2 + ( dz dt ) 2 dt = Z b a r ( dr dt cos θ + r sin θ dt ) 2 + ( dr dt sin θ - r cos θ dt ) 2 + ( dz dt ) 2 dt = Z b a r ( dr dt ) 2 + r 2 ( dt ) 2 + ( dz dt ) 2 dt Sec 14.1 20. f ( x, y ) = p x 2 + y 2 - 4 The domain is
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This note was uploaded on 09/30/2010 for the course MATH 100 taught by Professor Qt during the Fall '09 term at HKUST.

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