MAC 2313 Midterm: MAC 2313 FIU Exam 315k
15 Feb 2019
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Prof. s. hudson: let w = 4x2 + 4y2 + z2. Leave your answer in terms of , , , the usual spherical coordinates: [15pts] evaluate this integral by reversing the order of integration. 0 z 1 y/2 ex2 dx dy: find parametric equations for the surface z = e x2 in cylindrical coordinates). Use a triple integral to nd the volume of g: let g be a sphere of radius 5 centered at the origin. Use a triple integral in spherical coordinates to nd the volume of g: [20pts] true-false. Assume f , fx etc are di erentiable on rn (usually this is r2). If p is a critical point of f and d = fxxfyy (fxy)2 < 0 at p , then f has a relative extremum at p . Fubini"s theorem is mainly used to solve optimization problems. Converting from rectangular coordinates to spherical, the jacobian is 2 sin .
