Question 1

Find an equation for the function   whose derivative is   and whose graph passes through the point   . ​

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 2

Find ​   if   . ​

Accepted Answer

A) ​   
B) ​   
C) ​   
D) ​   
A) ​   
B) ​   
C) ​   
D) ​

Question 3

Suppose a population of bacteria is changing at a rate of   ,where t is the time in days.The initial population (when   )is 1,500.Write an equation that gives the population at any time t. ​

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 4

The graph of the function   is given below.Which of the following definite integrals yields the area of the shaded region? ​   ​

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 5

Find the general solution of the differential equation below and check the result by differentiation. ​   ​

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 6

Use the limit process to find the area of the region between the graph of the function   and x-axis over the interval   . ​

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 7

Find the integral   . ​

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 8

Find the indefinite integral of the following function. ​   ​

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 9

Use the properties of summation and Theorem 5.2 to evaluate the sum. ​   ​

Accepted Answer

A) 416 
B) 30,996 
C) 30,884 
D) 7,854 
E) 30,856 
A) 416 
B) 30,996 
C) 30,884 
D) 7,854 
E) 30,856

Question 10

A ball is thrown vertically upwards from a height of 10 ft with an initial velocity of 40 ft per second.How high will the ball go? Note that the acceleration of the ball is given by   feet per second per second.Round your answer to 4 decimal places. ​

Accepted Answer

A) 28.7500 ft 
B) 65.0000 ft 
C) 87.6000 ft 
D) 85.0000 ft 
E) 35.0000 ft 
A) 28.7500 ft 
B) 65.0000 ft 
C) 87.6000 ft 
D) 85.0000 ft 
E) 35.0000 ft

Question 11

Find the indefinite integral   . ​

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 12

Find the indefinite integral of the following function and check the result by differentiation. ​   ​

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 13

Evaluate the following definite integral by the limit definition. ​   ​

Accepted Answer

A)    
B)    
C)    
D)    
E) 15 
A)    
B)    
C)    
D)    
E) 15

Question 14

Suppose the demand equation for a product is   .Find the average price p on the interval   .Round your answer to the nearest dollar. ​

Accepted Answer

A) $42 
B) $756 
C) $832 
D) $76 
E) $69 
A) $42 
B) $756 
C) $832 
D) $76 
E) $69

Question 15

Solve the differential equation. ​   ,   ​

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 16

Find the indefinite integral. ​   ​

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 17

Let R be the region between the function   the x-axis,and the lines   and   .Using the Trapezoidal Sum,compute the area when there are four equal subdivisions.​ ​

Accepted Answer

A) ​221 
B) ​328 
C) ​228 
D) ​74 
A) ​221 
B) ​328 
C) ​228 
D) ​74

Question 18

Evaluate the integral   . ​

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 19

Find the indefinite integral. ​   ​

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 20

The force F (in newtons)of a hydraulic cylinder in a press is proportional to the square of sec x where x is the distance (in meters)that the cylinder is extended in its cycle.The domain of F is   and   .Find F as a function of x. ​

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Find an equation for the function whose derivative is and whose graph passes through the point .

Find if .

Suppose a population of bacteria is changing at a rate of ,where t is the time in days.The initial population (when )is 1,500.Write an equation that gives the population at any time t.

The graph of the function is given below.Which of the following definite integrals yields the area of the shaded region?

Find the general solution of the differential equation below and check the result by differentiation.

Use the limit process to find the area of the region between the graph of the function and x-axis over the interval .

Find the integral .

Find the indefinite integral of the following function.

Use the properties of summation and Theorem 5.2 to evaluate the sum.

A ball is thrown vertically upwards from a height of 10 ft with an initial velocity of 40 ft per second.How high will the ball go? Note that the acceleration of the ball is given by feet per second per second.Round your answer to 4 decimal places.

Find the indefinite integral .

Find the indefinite integral of the following function and check the result by differentiation.

Evaluate the following definite integral by the limit definition.

Suppose the demand equation for a product is .Find the average price p on the interval .Round your answer to the nearest dollar.

Solve the differential equation. ,

Find the indefinite integral.

Let R be the region between the function the x-axis,and the lines and .Using the Trapezoidal Sum,compute the area when there are four equal subdivisions.

Evaluate the integral .

Find the indefinite integral.

The force F (in newtons)of a hydraulic cylinder in a press is proportional to the square of sec x where x is the distance (in meters)that the cylinder is extended in its cycle.The domain of F is and .Find F as a function of x.

Preparation for Calculus

Limits and Their Properties

Differentiation

Applications of Differentiation

Differential Equations

Applications of Integration

Integration Techniques, L'Hôpital's Rule, and Improper Integrals

Infinite Series

Parametric Equations, Polar Coordinates, and Vectors

Mechanical Ventilation and Sedation: Assessment, Medications, and Complications

Filters

Exam 5: Integration

Find an equation for the function whose derivative is and whose graph passes through the point . ​

Find ​ if . ​

Suppose a population of bacteria is changing at a rate of ,where t is the time in days.The initial population (when )is 1,500.Write an equation that gives the population at any time t. ​

The graph of the function is given below.Which of the following definite integrals yields the area of the shaded region? ​ ​

Find the general solution of the differential equation below and check the result by differentiation. ​ ​

Use the limit process to find the area of the region between the graph of the function and x-axis over the interval . ​

Find the integral . ​

Find the indefinite integral of the following function. ​ ​

Use the properties of summation and Theorem 5.2 to evaluate the sum. ​ ​

A ball is thrown vertically upwards from a height of 10 ft with an initial velocity of 40 ft per second.How high will the ball go? Note that the acceleration of the ball is given by feet per second per second.Round your answer to 4 decimal places. ​

Find the indefinite integral . ​

Find the indefinite integral of the following function and check the result by differentiation. ​ ​

Evaluate the following definite integral by the limit definition. ​ ​

Suppose the demand equation for a product is .Find the average price p on the interval .Round your answer to the nearest dollar. ​

Solve the differential equation. ​ , ​

Find the indefinite integral. ​ ​

Let R be the region between the function the x-axis,and the lines and .Using the Trapezoidal Sum,compute the area when there are four equal subdivisions.​ ​

Evaluate the integral . ​

Find the indefinite integral. ​ ​

The force F (in newtons)of a hydraulic cylinder in a press is proportional to the square of sec x where x is the distance (in meters)that the cylinder is extended in its cycle.The domain of F is and .Find F as a function of x. ​

Preparation for Calculus

Limits and Their Properties

Differentiation

Applications of Differentiation

Differential Equations

Applications of Integration

Integration Techniques, L'Hôpital's Rule, and Improper Integrals

Infinite Series

Parametric Equations, Polar Coordinates, and Vectors

Mechanical Ventilation and Sedation: Assessment, Medications, and Complications

Filters

Find an equation for the function whose derivative is and whose graph passes through the point .

Find if .

Suppose a population of bacteria is changing at a rate of ,where t is the time in days.The initial population (when )is 1,500.Write an equation that gives the population at any time t.

The graph of the function is given below.Which of the following definite integrals yields the area of the shaded region?

Find the general solution of the differential equation below and check the result by differentiation.

Use the limit process to find the area of the region between the graph of the function and x-axis over the interval .

Find the integral .

Find the indefinite integral of the following function.

Use the properties of summation and Theorem 5.2 to evaluate the sum.

A ball is thrown vertically upwards from a height of 10 ft with an initial velocity of 40 ft per second.How high will the ball go? Note that the acceleration of the ball is given by feet per second per second.Round your answer to 4 decimal places.

Find the indefinite integral .

Find the indefinite integral of the following function and check the result by differentiation.

Evaluate the following definite integral by the limit definition.

Suppose the demand equation for a product is .Find the average price p on the interval .Round your answer to the nearest dollar.

Solve the differential equation. ,

Find the indefinite integral.

Let R be the region between the function the x-axis,and the lines and .Using the Trapezoidal Sum,compute the area when there are four equal subdivisions.

Evaluate the integral .

Find the indefinite integral.

The force F (in newtons)of a hydraulic cylinder in a press is proportional to the square of sec x where x is the distance (in meters)that the cylinder is extended in its cycle.The domain of F is and .Find F as a function of x.