1.

Determine which of the following series converge:

2.

Find the exact sum of the following series:

3.

Determine the interval of convergence of the following series:

4.

Find the exact length of the graph of the following function:

5.

The base of a solid is the region bounded by y² = 4ax and x = a. Each cross section perpendicular to the x-axis is an equilateral triangle. Find the volume of the solid.

6.

A right circular conical tank, point down, with top radius 5 ft and height 10 ft, is filled with a liquid of density 60 lb/ft³. Find the work done in pumping the liquid to a trough located 2 ft above the tank. If the pump is run by a 1/2 horsepower motor, how long will it take to empty the tank? ( One horsepower is 550 ft-lbs per second.)

7.

A certain rectangular pool is 50 ft long, 30 ft wide, and 10 ft deep. A triangular drain plate is positioned at the bottom of one of the sides which is 30 ft by 10 ft. The plate itself is 2 ft wide, 1 ft high, and positioned vertex down. Water is running into the tank at the rate of 1000 ft³/hr.

(a)

Find the force against the triangular plate after 9 hours of filling.

(b)

The plate is designed to withstand a force of 520 lb. How high can the pool be filled without exceeding this design limitation?