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Unformatted text preview: J , ~ A J (I  2~ + 2) !A x xL 3) Given F ( x ) = ( + eY)& , find dFldx in two ways: a) by differentiating fust and b) by Y integrating first. ( .? marks) Page 4 of 7 4) Use a triple integral in spherical coordinates to find the volume of the solid common to the spheres p = 2&cos( and p = 2 . (1 0 marks) Page 5 of 7 L 5 ) Find the surface area of the part of the saddle az = 2  3 inside the cylinder 2 + J? = a2, a > 0, by means of a double integral over the projected area. . lice, . (6 marks) .*. Try Page 6 of 7 6) Let F '(x) = f(x) and G '(x) = g(x) on the interval asxs b. Let T be the triangle with vertices (I, a), (b, a) and (b, b). By integrating 11 f (x)&)d~ in both orders, show that: T (This is an alternate derivation of the formula for integration by parts.) (10 marks) Page 7 of 7...
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 Fall '08
 J.Davis
 MAT293F VECTOR CALCULUS, J. W. Davis

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