Chapter 14.7, Problem 32E

Assuming that the rate of change of the price P of a certain commodity is proportional to the difference between demand D and supply S at any time t, the differential equations describing the price fluctuations with respect to time can be expressed as: dP/dt = k(D - s) where k is the proportionality constant whose value depends on the specific commodity. Solve the above differential equation by expressing supply and demand as simply linear functions of price in the form S = aP - b and D = e - fP

Find the area of the surface obtained by rotating the circle x² + y² = r² about the line y = r.

1) Find the equation of the tangent line to the graph y=xe at the point (1, 1).