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tutorial8 - 2. ( § 5.5 no.11) Evaluate RR D (2 x + y ) 2 e...

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MATH1211/10-11(2)/Tu8/TNK THE UNIVERSITY OF HONG KONG DEPARTMENT OF MATHEMATICS MATH1211 Multivariable Calculus 2010-11 2nd Semester: Tutorial 8 Date of tutorial classes: March 31–April 1. (The section/problem numbers in the following refer to those in the textbook.) 1. (Variation of § 5.4 no.8(b)) Use triple integral to find the volume of the region bounded by the surfaces y = x 2 + z 2 and y = 9 - x 2 - z 2 . ( Hint : You may use change of variables if necessary.)
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Unformatted text preview: 2. ( § 5.5 no.11) Evaluate RR D (2 x + y ) 2 e x-y dA , where D is the region enclosed by 2 x + y = 1 , 2 x + y = 4 , x-y =-1, and x-y = 1. 3. ( § 5.6 no.4) Find the average value of g ( x,y,z ) = e z over the unit ball given by B = { ( x,y,z ) | x 2 + y 2 + z 2 ≤ 1 } . 4. ( § 6.1 no.2) Calculate R x f ds where f ( x,y,z ) = xyz , x ( t ) = ( t, 2 t, 3 t ), 0 ≤ t ≤ 2. 1...
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