Exam 16: Methods and Applications of Integration

Either find the value of or show that it diverges.

Determine the value of the constant k so that = 1.

Use the formula + C to find

Solve the differential equation: y' = ,y > 0

Use the tables to find:

Suppose the membership in a new country club is to be a maximum of 1,000 persons.One year ago,the initial membership was 100 persons and now there are 500.Suppose the enrollment follows a logistic function,i.e., How many members will there be three years from now?

A rumor is circulating in a city whose population is 20,000.At the beginning of the month 50 people know of the rumor,and one week later 200 know of it.Assuming logistic growth,the number N of people who know the rumor t weeks after the beginning of the month is given by

Determine if converges or diverges.If it converges,to what number does it converge?

Solve the differential equation: y' = 3 y

The rate of seepage from a toxic waste dump is R(t)= ,where t is the time in years and R(t)is the number of gallons of toxic waste.Find ,the total amount of waste that will seep from the dump.

=

Determine if converges or diverges.If it converges,to what number does it converge?

Solve the differential equation: ( + 3x + 1) = y(2x+ 3),y(0)= 2

Suppose that the accompanying table shows the velocity of a car every second for 8 seconds.Use the Trapezoidal Rule to approximate the distance traveled by the car in the 8 seconds.

Find the exact area of the region bounded by the graphs of y = 8 - 2x - and y = 3x + 2.Also sketch the region.

Use the tables to find:

Solve the differential equation = if x > 0 and y > 0.

Use the formula = + C to find .

If = Where x > 0 and y > 0,then y =

Find the exact area of the region bounded by the graphs of x = and x - y - 2 = 0.Also sketch the region.