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quiz2practice - The University of Sydney School of...

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Unformatted text preview: The University of Sydney School of Mathematics and Statistics Practice questions for the vector calculus quiz MATH2061/2067: Vector Calculus Semester 1, 2011 These are practice questions only. The actual test will have 15 multiple choice questions and the time allowed will be 40 minutes . At the back of the Question Paper you will find a Formula Sheet and a Table of Standard Integrals. 1. Find ∇· F if F = xy i + y 2 j + e 2 z k . 2. Find ∇ φ if φ = x 2 yz . 3. Write an equation in vector form for the straight line which passes through the points (1 , − 1 , 2) and (5 , 3 , − 1). 4. Find ∇× F if F = 2 xy i − 7 j + 2 y k . 5. Given that F = y cos xy i + x cos xy j − 3 k is conservative find a potential function for F . 6. Find a vector normal to the plane x − 3 y + 4 z = 0. 7. Describe in polar coordinates the region in the plane bounded by the circles x 2 + y 2 = 4 and x 2 + y 2 = 9, with y ≤ 0....
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