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

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

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Unformatted text preview: Math 22 - Review 2 Answers - Winter 11 t t t t 1.) r (t) =< ( √2 + 1) cos(ln( √2 + 1)) , 1 , ( √2 + 1) sin(ln( √2 + 1)) > 2.) κ(t) = 18/61 3.) (− 1 ln(2), 2 1 √) 2 4.)(a.) x + 2y + 3z = 6 (b.) 3x − 3y + z = 1 5.) (a.) Show. (b.) ln(3) − 6.) (a.) √ 53 g 1 2 75 km (b.) 3.g km 7.) The projectile lands 600 g2 m east and √ 200 3 g m north of where it was launched. 8.) (5, 15, 2) and (19, 133, 12) 9.)(a.) fx (x, y ) = 5x4 y 3 + 6xy 4 , fy (x, y ) = 3x5 y 2 + 12x2 y 3 (b.) fx (x, y ) = y 3 −x2 y 2 , (x2 +y )2 fy (x, y ) = 2x3 y +xy 2 (x2 +y )2 (c.) fx (x, y, z ) = y tan−1 (y 2 z ), fy (x, y, z ) = x tan−1 (y 2 z ) + 2xy 2 z , 1+y 4 z 2 fz (x, y, z ) = (d.) fx (x, y, z, t) = −zeyz+t sin(xz ), fy (x, y, z, t) = zeyz+t cos(xz ), fz (x, y, z, t) = eyz+t (y cos(xz ) − x sin(xz )), ft (x, y, z, t) = eyz+t cos(xz ) 10.) fxx (x, y ) = 24 sin(2x + 3y ) cos2 (2x + 3y ) − 12 sin3 (2x + 3y ) fyy (x, y ) = 54 sin(2x + 3y ) cos2 (2x + 3y ) − 27 sin3 (2x + 3y ) fxy (x, y ) = fyx (x, y ) = 36 sin(2x + 3y ) cos2 (2x + 3y ) − 18 sin3 (2x + 3y ) 11.) fxyz (x, y, z ) = 12.) dw dt = ∂3 12 , ∂y2 f (2y +3z )3 ∂z x cos(t)−y sin(t)+z sec2 (t) x2 +y 2 +z 2 = −72x (2y +3z )4 = tan(t) 13.) ∂w/∂s = 2x sin(y ) + x2 t cos(y ) + y 2 exy + xytexy + texy ∂w/∂t = 4x sin(y ) + x2 s cos(y ) + 2y 2 exy + xysexy + sexy 14.) 19/5 √ 15.) 14 ; direction specified by < 1, 2, 3 > 16.) 4x − 5y − z = 4 w(x, y, z ) = z xyz < yz ln(z ) , xz ln(z ) , xy ln(z ) + xy > √ 18.) 7/ 17 17.) 19.) x = 5 + 8t , y = −1 + 53t , z = 2 + 11t 20.) (2, 1 , −1) and (−2, − 1 , 1) 2 2 xy 3 1+y 4 z 2 ...
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This note was uploaded on 04/09/2012 for the course MATH 22 taught by Professor Castro during the Winter '08 term at UCSC.

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