Optimization Problems:
a)How close does the line y=1+2x come to the origin?
b) Find the dimensions of a right circular cylinder that is open on the top, isolated on the bottom, holds 1 liter, and uses the least amount of material.
c) A circular sector with radius r and angle (theta) has area A. Find r and theta so that the perimeter is smallest for a given area A. (Note: A=(1/2)*r*theta, and the length of the arc s=r*theta, when theta is measured in radians)