Each problem is worth 5 points.

1. (a) Have a computer generate a good picture of the graph of x⁴+y⁴+z⁴=1. Describe the surface in a couple of sentences -- pretend you're trying to describe it to somebody over the phone, and try to convey its appearance as well as you can.

(b) Find the volume of the region contained inside the relation from part (a).
 
 

2. [Stewart 13.3 #28] Write a double integral for and compute the volume of the region bounded by the cylinders x²+y²=r² and y²+z²=r².
 
 

3. [Stewart 13.3 #32] Write a double integral for and find the exact value of the volume between z=2x²+y² and z=8-x²-2y² and inside the cylinder x²+y²=1.
 
 

4. Find the volume of the region in the first octant bounded by x+y=1, x+z=1, and y+z=1.
 
 

5. Set up a double integral and find the volume between the plane z=0 and the surface z=a-x²-y² in terms of a.