Problem 1

Find the limit or show that it does not exist

We can see the solution depends on the angle of approach and thus there is not solution.

Problem 2

A certain solid is a right-circular cylinder. Its base is the disk of radius 2 centred at the origin in the -plane. It has a height 2 and a density .

A smaller solid is obtained by removing the inverted cone, who's base is the top of the surface and who's vertex is at the point .

(a). Use Cylindrical Coordinates to Set up an Integral Giving the Mass of

(b). Use Spherical Coordinates to Set up an Integral Giving the Mass of

(c). Find the Mass of

Problem 3

A solid is bounded below by the cone and above by the sphere . It has a density .