1.(10)  ò[([Ö(1-x²)])/( x²)]dx

2.(10)  ò[(3x)/( [Ö(4+x²)])]dx

3.(30)  Find the volumes of the solids of revolution.  (Set up integrals.)  Tell the method you use.  Use disks/washers at least once.  Use shells at least once.

a)  Region I about the x-axis
b)  Region II about the vertical line x = [(p)/ 2]
c)  Region III about the horizontal line y = 2.

4.(10)  A 100 pound load is being pulled up a 30 foot tower by a chain weighing 4 pounds per foot.  Set up integrals to
a)  find the amount of work needed to raise the load the first 10 feet.   
b)  find the amount of work needed to raise the load the last 10 feet.

5.(10)  A flood gate in a dam is in the shape of half a disk (think of the top half of a circle).  The half disk has a radius of 5 ft.  The top of the gate is located 20 feet below the water line.  Set up an integral to find the force due to water pressure on the gate.

6.(10)  Find the cubic Taylor polynomial P₃(x) for f(x) = sinx expanded about a = [(p)/ 3].

7.(10) a) Calculate the third partial sum, s₃, for the series  å_{k = 1}^¥[2/( k²+1)].  (Nothing fancy here; I am checking to see if you know the definition of partial sum.)
b)  This series is not telescoping.  Why not?
c)  This series is not geometric.  Why not?

8.(10)  Suppose the series  å_{k = 1}^¥ a_k has partial sums  s_n = [(3n(n+1))/( 4n²-1)].
a)  Is the series å_{k = 1}^¥ a_k convergent or divergent?  Explain.
b)  If convergent, what is the sum of the series?  Explain.