MATH 200 Study Guide - Midterm Guide: Spherical Coordinate System, Cylindrical Coordinate System, Directional Derivative

• School: UBC
• Department: Mathematics
• Course: MATH 200
• Professor: All

Document Summary

2: [10pts] let e be the region bounded between the parabolic surfaces z = x2 + y2 and z = 2 x2 y2 and within the cylinder x2 + y2 1. Calculate the integral of f (x, y, z) = (x2 + y2)3/2 over the region e: [10pts] match the following equations and expressions with the corresponding pictures. Cartesian coordi- nates are (x, y, z), cylindrical coordinates are (r, , z), and spherical coordinates are ( , , ). = 2 cos r = 2 cos y = x2 + z2 z = x4 + y4 4xy . 3: [10pts] write the integral given below 5 other ways, each with a di erent order of integration. You may nd some of the following trig identities useful: cos(a + b) = cos(a) cos(b) sin(a) sin(b) sin(a + b) = sin(a) cos(b) + cos(a) sin(b) cos(2a) = 2 cos2(a) 1 cos2(a) =