Question 1

Either find the value of  
or show that it diverges.

Accepted Answer

The answer of Either find the value of  
or...

Question 2

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

Accepted Answer

The answer of Determine the value of the constant k...

Question 3

Use the formula  
+ C to find

Accepted Answer

The answer of Use the formula  
+ C to...

Question 4

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

Accepted Answer

The answer of Solve the differential equation: y' = ...

Question 5

Use the tables to find:

Accepted Answer

The answer of Use the tables to find: ...

Question 6

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?

Accepted Answer

The answer of Suppose the membership in a new country...

Question 7

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

Accepted Answer

A)  N = 20,000  
B)  N =  
C)  N =  
D)  N =  
E)  none of the above

Question 8

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

Accepted Answer

The answer of Determine if  
converges or diverges.If it...

Question 9

Solve the differential equation: y' = 3  
y

Accepted Answer

The answer of Solve the differential equation: y' = 3...

Question 10

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.

Accepted Answer

The answer of The rate of seepage from a toxic...

Question 11

=

Accepted Answer

A)   
B)  -  
C)   
D)  -  
E)  integral diverges

Question 12

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

Accepted Answer

The answer of Determine if  
converges or diverges.If it...

Question 13

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

Accepted Answer

The answer of Solve the differential equation: (  
+...

Question 14

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.

Accepted Answer

A)  145.5 feet 
B)  291 feet 
C)  162 feet 
D)  221.5 feet

Question 15

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

Accepted Answer

The answer of Find the exact area of the region...

Question 16

Use the tables to find:

Accepted Answer

The answer of Use the tables to find: ...

Question 17

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

Accepted Answer

The answer of Solve the differential equation  
= ...

Question 18

Use the formula  
=  
+ C to find  
.

Accepted Answer

The answer of Use the formula  
=  
+...

Question 19

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

Accepted Answer

A)  ln(x) + C. 
B)   ln(x) + C. 
C)   
D)   
E)

Question 20

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

Accepted Answer

The answer of Find the exact area of the region...

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.