I need help with these fast, it's for homework and I don't get it and my homework is due at midnight tonight.
1. Find the dimensions of the right circular cylinder with greatest volume that can be contained in a sphere of radius 1.
2. What is the largest (by area) rectangle with sides parallel to the coordinate axes that can be contained in the region of the plane bounded by the graphs of y=0, y=x (1-E^(x/x-1)) and x=1?