Quiz2A-2011

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Unformatted text preview: The University of Sydney School of Mathematics and Statistics Solutions to Vector Calculus - Quiz A MATH2061/2067: Semester 1, 2011 1. Let F = 2x i + y j. Find the flux C F n ds, where C is the unit circle, centre (0, 0), taken once anti-clockwise, and n the unit outward normal. (a) 0 Solution: (c) 2. Which of the following integrals gives the volume of the solid enclosed between the paraboloid z = 1 - x2 - y 2 , z 0, and the xy-plane ? =2 r=1 =2 r=1 (b) /2 (c) 3 (d) 2. (a) =0 =2 r=0 r=1 r=0 r 2 dr d (1 - r 2 )r dr d (b) =0 =2 r=0 r=1 r=0 (1 - r 2 )1/2 r dr d (1 - r 2 )1/2 dr d. (c) =0 (d) =0 Solution: (c) 3. Find a potential function of the gradient field F = (y 2 - (sin x)ez ) i + 2xy j + (cos x)ez k. (a) xy 2 + (sin x)ez (c) 2xy - (sin x)ez Solution: (d) 4. Evaluate gram. y 1 (b) 2xy + (sin x)ez - (cos x)ez (d) xy 2 + (cos x)ez . (x + 2y) dA where R is the shaded region shown in the diaR 1 x (a) 1/2 (b) 4/3 (c) 3/2 (d) 2/3. Solution: (a) Copyri...
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This note was uploaded on 02/06/2012 for the course MATH 2061 taught by Professor Notsure during the Three '09 term at University of Sydney.

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