SecBEx4W01 - (2(d Is there a function such that Explain f F...

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EXAM 4 MATH 22 Name: ____________________________ Winter 2001 Section: __________ You have 50 minutes to complete this test. You must show all work to receive full credit. 1. Given the vector field F x y x y x y i xy x y j = + + + + + ( , ) ( ) ( ) 2 3 2 3 2 2 3 2 (4) (a) Determine whether or not is a conservative vector field. F (10) (b) If is conservative, find a function such that . F f F f = ∇ (4) (c) Use part (b) to evaluate where is the arc of the curve from F d r C . C y x x = sin to . ( , ) 0 0 ( , ) p 0 (12) 2. Evaluate where is the positively oriented ( tan ) ( ) x x dx x y dy C 2001 2 2001 5 4 + + + C boundary of the region enclosed by the curves , , . (Hint: Green’s thm.) y x = x = 1 y = 0 3. Let be the path consisting of the parabolic arc from to . Calculate the C y x = 2 2 ( , ) 0 0 ( , ) 1 1 2 line integrals: (7) (a) , (7) (b) 3 xdS C 6 3 ydx xdy C + 4. Consider the vector field . (6) (a) Find F x y z zx y z =< ( , , ) , , 2 2 2 curlF (4) (b) Find , (4) (c) Find div F ∇ ∇ .( ) x F
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Unformatted text preview: (2) (d) Is there a function such that ? ( Explain.) f F f → = ∇ (14) 5. Find an equation of the tangent plane at the point to the parametric ( , , ) ( , , ) x y z = 4 4 2 surface given by , , . S r u v v uv u → =< ( , ) , , 2 3 ≤ ≤ u- ≤ ≤ 3 3 v (12) 6. Set up, but do NOT evaluate , an iterated integral to find the area of the part of the surface that lies above the triangle with vertices , , . z x y = + 2 2 1999 ( , ) 1 0 ( , ) 11 ( , ) 2 0 (14) 7. Set up, but do NOT evaluate , the surface integral to find the flux, , of the vector F dS S → → ∫∫ . field across , where is given by the parametric equation F x y z y i x j z k → → → → = + + ( , , ) 2 S S , , with upward orientation. r u v u v u v v → =< ( , ) cos , sin , 1 ≤ ≤ u ≤ ≤ v p...
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This note was uploaded on 01/24/2011 for the course MATH 22 taught by Professor Brigham during the Winter '08 term at Missouri S&T.

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SecBEx4W01 - (2(d Is there a function such that Explain f F...

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