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Math+22+-+Review+2+Answers+-+Winter+11

# Math+22+-+Review+2+Answers+-+Winter+11 - Math 22 Review 2...

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Math 22 - Review 2 Answers - Winter 11 1.) r ? ( t ) = < ( t 2 + 1) cos(ln( t 2 + 1)) , 1 , ( t 2 + 1) sin(ln( t 2 + 1)) > 2.) κ ( t ) = 18 / 61 3.) ( - 1 2 ln(2) , 1 2 ) 4.)(a.) x + 2 y + 3 z = 6 (b.) 3 x - 3 y + z = 1 5.) (a.) Show. (b.) ln(3) - 1 2 6.) (a.) 5 3 g km (b.) 3 . 75 g km 7.) The projectile lands 600 g 2 m east and 200 3 g m north of where it was launched. 8.) (5 , 15 , 2) and (19 , 133 , 12) 9.)(a.) f x ( x, y ) = 5 x 4 y 3 + 6 xy 4 , f y ( x, y ) = 3 x 5 y 2 + 12 x 2 y 3 (b.) f x ( x, y ) = y 3 - x 2 y 2 ( x 2 + y ) 2 , f y ( x, y ) = 2 x 3 y + xy 2 ( x 2 + y ) 2 (c.) f x ( x, y, z ) = y tan - 1 ( y 2 z ), f y ( x, y, z ) = x tan - 1 ( y 2 z ) + 2 xy 2 z 1+ y 4 z 2 , f z ( x, y, z ) = xy 3 1+ y 4 z 2 (d.) f x ( x, y, z, t ) = - ze yz + t sin( xz ), f y ( x, y, z, t ) = ze yz + t cos( xz ), f z ( x, y, z, t ) = e yz + t ( y cos( xz ) - x sin( xz )), f t ( x, y, z, t ) = e yz + t cos( xz ) 10.) f xx ( x, y ) = 24 sin(2 x + 3 y ) cos 2 (2 x + 3 y ) - 12 sin 3 (2 x + 3 y ) f yy ( x, y ) = 54 sin(2 x + 3 y ) cos 2 (2 x + 3 y ) - 27 sin 3 (2 x + 3 y ) f xy ( x, y ) = f yx ( x, y ) = 36 sin(2 x + 3 y ) cos 2 (2 x + 3 y ) - 18 sin 3 (2 x + 3 y ) 11.) f xyz ( x, y, z ) = 12
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