MATH 222 Final: MATH 222 KSU TestFinalU11

• School: Kansas State University
• Department: Mathematics
• Course: MATH 222
• Professor: All

Document Summary

To receive credit you must show your work (20 pts) problem 1. Find the extreme values of the function on the disk f (x, y) = x2 + 2y2 x2 + y2 1. Use a double integral to nd the volume of the solid which is bounded by the surfaces z = xy3 + 2. 1+y , z = xy3, x = 1 y2, and the planes y = x 1, y = 1. Use cylindrical coordinates to set up an integral (but do not solve, i. e. , do. Use spherical coordinates to set up a integral (but do not solve, i. e. , do. Not compute the integrals) for computing: the volume of the solid which is in the rst octant, inside the spheres x2 + y2 + z2 = 2 and above the plane z = 1. Find the area of the surface s which is the part of the plane.