Each problem is worth 2 points. For full credit indicate clearly how you reached your answer.

1. Compute .

2. If f(x) = kx³ - sin x + e ^x, find f(x).

3. If y = x tan x -  + cos³ x, find .

4. [Based loosely on Stewart 15.1 #45] A thin metal plate, located in the xy-plane, has temperature T(x,y) at the point (x,y), where x and y are measured in meters. The level curves of T are called isothermals because at all points on an isothermal he temperature is the same. If the temperature function (in degrees celsius) is given by T(x,y) = 100/(1+x²+2y²), describe (precisely, in words) the region where the temperature is at least 20 degrees.

5. Consider a cylinder with a radius r, and suppose water falls into the cylinder at a rate of 1 liter per minute. Give a formula for d(r,t), the depth of the water after t minutes.