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Unformatted text preview: Please write out the honor pledge and sign it: NAME (print): Instructor / class section: MAT 203 – Quiz 3 Due: Monday, November 23, 2009 Information Please read and sign the exam conditions first before turning the page: • No books / notes / calculators / collaborations are allowed. • The quiz has to be completed in a single time stretch of 20 min . No interruptions ! • Please STAPLE your answer sheets, with this problem sheet as the front page. Write your full name legibly on every sheet. I have read these conditions and will follow them (initials): Score: Problem 1: points Problem 2: points 1 Problem 1 (5 points) Let D be the planar domain D = ( x,y ) | x 2 + ( y- 1 / 2) 2 ≤ 1 / 4 and 0 ≤ x ≤ y . Draw D and calculate the double integral ZZ D x 2 x 2 + y 2 dA. Solution: Using polar coordinates, we observe that x 2 + ( y- 1 / 2) 2 ≤ 1 / 4 is equivalent to r 2 ≤ r sin θ and f ( x,y ) = x 2 x 2 + y 2 is transformed to f ( r cos θ,r sin θ ) = cos 2 θ . It follows that....
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- Sin, Cos, Spherical coordinate system, Multiple integral