Test Bank Docx Chapter 6 Antiderivatives And Applications

Applied Calculus, 7e (Hughes-Hallett)

Chapter 6 Antiderivatives and Applications

6.1 Analyzing Antiderivatives Graphically and Numerically

1) Suppose (x) = 4x + 3 and F(0) = 1. Find the value of F(5).

Diff: 2 Var: 1

Section: 6.1

Learning Objectives: Estimate values of a function numerically given information on its derivative.

2) Suppose (x) = and F(0) = -3. Estimate the value of F(5) to 4 decimal places.

Diff: 2 Var: 1

Section: 6.1

Learning Objectives: Estimate values of a function numerically given information on its derivative.

3) Suppose (x) = and F(0) = 3. Estimate the value of F(5) to 4 decimal places.

Diff: 2 Var: 1

Section: 6.1

Learning Objectives: Estimate values of a function numerically given information on its derivative.

4) Suppose (x) = -10x + 8 and F(5) = -80. Find the value of F(3).

Diff: 2 Var: 1

Section: 6.1

Learning Objectives: Estimate values of a function numerically given information on its derivative.

5) This figure shows the rate of change of F.

Given that F(0) = 2, sketch the graph of F.

Diff: 1 Var: 1

Section: 6.1

Learning Objectives: Sketch the graph of a function given information on its derivative.

6) This figure shows the rate of change of F.

Given that F(0) = 2, sketch the graph of F.

Diff: 2 Var: 1

Section: 6.1

Learning Objectives: Sketch the graph of a function given information on its derivative.

7) The graph of the derivative F' of a function F is shown. Assuming that estimate the maximum value attained by F.

Diff: 2 Var: 1

Section: 6.1

Learning Objectives: Estimate values of a function numerically given information on its derivative.

8) Choose the function that would correspond to this graph of .

A)

B)

C)

D)

Diff: 1 Var: 1

Section: 6.1

Learning Objectives: Sketch the graph of a function given information on its derivative.

9) Choose the function that would correspond to this graph of .

A)

B)

C)

D)

Diff: 1 Var: 1

Section: 6.1

Learning Objectives: Sketch the graph of a function given information on its derivative.

10) The following figure shows the graph of f (x). If = f and F(0) = 3, find F(1).

Diff: 1 Var: 1

Section: 6.1

Learning Objectives: Estimate values of a function numerically given information on its derivative.

11) The following figure is a graph of (x). On which of the following intervals is f decreasing?

A) -2 < x < 1 B) 1 < x < 3 C) 0 < x < 2 D) -0.8 < x < 3

Diff: 1 Var: 1

Section: 6.1

Learning Objectives: Sketch the graph of a function given information on its derivative.

12) Given the following graph of (x) and the fact that g(0) = 2000, find g(400).

Diff: 1 Var: 1

Section: 6.1

Learning Objectives: Estimate values of a function numerically given information on its derivative.

13) Given the following graph of (x) and the fact that g(0) = 2000, determine whether g (50) is positive or negative.

Diff: 1 Var: 1

Section: 6.1

Learning Objectives: Estimate values of a function numerically given information on its derivative.

14) Given the following graph of (x) and the fact that g(0) = 2000, what is x = 300?

A) a local minimum B) a local maximum

C) an inflection point D) none of the above

Diff: 1 Var: 1

Section: 6.1

Learning Objectives: Estimate values of a function numerically given information on its derivative.

15) The following graph represents the rate of change of a function f with respect to x; i.e., it is the graph of , with Which of the following are true at Select all that apply.

A) f is concave up. B) f is concave down.

C) f is increasing. D) f is decreasing.

Diff: 2 Var: 1

Section: 6.1

Learning Objectives: Sketch the graph of a function given information on its derivative.

16) The following graph represents the rate of change of a function f with respect to x; i.e., it is the graph of , with Find a value a to one decimal place such that and If there is no such value, enter "none".

Diff: 2 Var: 1

Section: 6.1

Learning Objectives: Estimate values of a function numerically given information on its derivative.

17) The following figure shows the graph of (x). If f (0) = 100, find f (30).

Diff: 1 Var: 1

Section: 6.1

Learning Objectives: Estimate values of a function numerically given information on its derivative.

18) Given the values of(x) in the table and that f (0) = 40, estimate f (6) to the nearest whole number.

Diff: 1 Var: 1

Section: 6.1

Learning Objectives: Estimate values of a function numerically given information on its derivative.

19) Using the following figure, find G(4) if G(0) = 10 and = g.

Diff: 2 Var: 1

Section: 6.1

Learning Objectives: Estimate values of a function numerically given information on its derivative.

20) The following figure shows the graph of f. If = f and F(0) = 0, find F(3).

Diff: 1 Var: 1

Section: 6.1

Learning Objectives: Estimate values of a function numerically given information on its derivative.

6.2 Antiderivatives and the Indefinite Integral

1) What is the antiderivative of f (x) = 9 + 3?

A) 3 + 3x + C B) 9 + 3x + C C) 18x + 3 + C D) 18x + C

Diff: 1 Var: 1

Section: 6.2

Learning Objectives: Find antiderivatives and indefinite integrals of functions.

2) What is the antiderivative of h(t) = ?

A) - + C B) 3 ln + C C) 3t ln + C D) + C

Diff: 2 Var: 1

Section: 6.2

Learning Objectives: Find antiderivatives and indefinite integrals of functions.

3) Find an antiderivative G(z) with (z) = g(z) and G(0) = 7, given that

A) - + 7 B) 6 -

C) - + 7 D) -

Diff: 2 Var: 1

Section: 6.2

Learning Objectives: Find antiderivatives and indefinite integrals of functions.

4) Find an antiderivative F(x) of f (x) = sin x such that F(0) = 4.

A) cos x B) -cos x + 3 C) cos x + 4 D) -cos x + 5

Diff: 2 Var: 1

Section: 6.2

Learning Objectives: Find antiderivatives and indefinite integrals of functions.

5) Find an antiderivative F(x) of f (x) = + 1 such that F(0) = 2.

A) + x + 1 B) + x + 3 C) + x D) x + x

Diff: 2 Var: 1

Section: 6.2

Learning Objectives: Find antiderivatives and indefinite integrals of functions.

6) Find an antiderivative F(x) of f (x) = + 3 such that F(1) = a, for some constant a.

A) - + 3x + a - 2 B) - + 3x + a

C) + 3x + a - 2 D) + 3x + a

Diff: 2 Var: 1

Section: 6.2

Learning Objectives: Find antiderivatives and indefinite integrals of functions.

7) Evaluate .

A) + 4 - 2x + C B) + 4 - 2x + C

C) + 8 - 2x + C D) + 8 - 2x + C

Diff: 1 Var: 1

Section: 6.2

Learning Objectives: Find antiderivatives and indefinite integrals of functions.

8) Evaluate .

A) ln + + C B) ln - + C

C) - + C D) + + C

Diff: 3 Var: 1

Section: 6.2

Learning Objectives: Find antiderivatives and indefinite integrals of functions.

9) Evaluate .

A) 3 + C B) + C C) 6 + C D) 2 + C

Diff: 2 Var: 1

Section: 6.2

Learning Objectives: Find antiderivatives and indefinite integrals of functions.

10) Find the indefinite integral .

A) + + 8p + C B) + + 8p + C

C) + 3 + 8p + C D) + 3 + 8p + C

Diff: 1 Var: 1

Section: 6.2

Learning Objectives: Find antiderivatives and indefinite integrals of functions.

11) Find the indefinite integral .

A) -sin θ + C B) sin θ + C C) cos θ + C D) + C

Diff: 1 Var: 1

Section: 6.2

Learning Objectives: Find antiderivatives and indefinite integrals of functions.

12) Find the indefinite integral .

A) + C B) + C

C) + C D) + C

Diff: 2 Var: 1

Section: 6.2

Learning Objectives: Find antiderivatives and indefinite integrals of functions.

13) = 2 + 3 - 3 + 5x + C

Diff: 1 Var: 1

Section: 6.2

Learning Objectives: Find antiderivatives and indefinite integrals of functions.

14) = -sin t + 5 cos t + C

Diff: 2 Var: 1

Section: 6.2

Learning Objectives: Find antiderivatives and indefinite integrals of functions.

15) = 2 + C

Diff: 2 Var: 1

Section: 6.2

Learning Objectives: Find antiderivatives and indefinite integrals of functions.

16) = + 8x + C

Diff: 2 Var: 1

Section: 6.2

Learning Objectives: Find antiderivatives and indefinite integrals of functions.

17) = - + C

Diff: 2 Var: 1

Section: 6.2

Learning Objectives: Find antiderivatives and indefinite integrals of functions.

18) Find the indefinite integral , where k is a constant.

A) k + C B) + C C) + C D) 2k + C

Diff: 1 Var: 1

Section: 6.2

Learning Objectives: Find antiderivatives and indefinite integrals of functions.

19) Find the indefinite integral , where k is a constant.

A) cos kθ + C B) - cos kθ + C

C) -k cos kθ + C D) cos kθ + C

Diff: 2 Var: 1

Section: 6.2

Learning Objectives: Find antiderivatives and indefinite integrals of functions.

20) Find the antiderivative of f (x) = + b, where a and b are constants.

A) + bx + C B) - + bx + C

C) a ln + bx + C D) ln + bx + C

Diff: 2 Var: 1

Section: 6.2

Learning Objectives: Find antiderivatives and indefinite integrals of functions.

21) Find a possible antiderivative of f (x) = , where a and b are constants.

A) B) -

C) D) -

Diff: 3 Var: 1

Section: 6.2

Learning Objectives: Find antiderivatives and indefinite integrals of functions.

22) Find an antiderivative F of f (x) = 2 cos x + sin x satisfying F(0) = 8.

A) F(x) = 2 sin x - cos x + 9 B) F(x) = 2 sin x - cos x

C) F(x) = -2 sin x - cos x + 7 D) F(x) = x + + 7

Diff: 2 Var: 1

Section: 6.2

Learning Objectives: Find antiderivatives and indefinite integrals of functions.

23) Evaluate.

A) + C B) + C C) + C D) + C

Diff: 1 Var: 1

Section: 6.2

Learning Objectives: Find antiderivatives and indefinite integrals of functions.

24) Evaluate.

A) ln + C B) - x + 3ln + C

C) + + C D) - x + + C

Diff: 2 Var: 1

Section: 6.2

Learning Objectives: Find antiderivatives and indefinite integrals of functions.

25) Find an antiderivative of - + .

A) - - + C B) - + + C

C) - 9 ln + + C D) - 9 ln - + C

Diff: 2 Var: 1

Section: 6.2

Learning Objectives: Find antiderivatives and indefinite integrals of functions.

6.3 Using the Fundamental Theorem to Find Definite Integrals

1) Evaluate .

Diff: 1 Var: 1

Section: 6.3

Learning Objectives: Use the Fundamental Theorem to calculate definite integrals exactly.

2) Use a definite integral to find the area under the graph of y = -2 + 3x + 5 between and Round to 2 decimal places.

Diff: 1 Var: 1

Section: 6.3

Learning Objectives: Use the Fundamental Theorem to calculate definite integrals exactly.

3) Find the average value of f (x) = + 1 on the interval to

Diff: 2 Var: 1

Section: 6.3

Learning Objectives: Use the Fundamental Theorem to calculate definite integrals exactly.

4) Evaluate .

Diff: 1 Var: 1

Section: 6.3

Learning Objectives: Use the Fundamental Theorem to calculate definite integrals exactly.

5) Evaluate .

Diff: 1 Var: 1

Section: 6.3

Learning Objectives: Use the Fundamental Theorem to calculate definite integrals exactly.

6) Evaluate . Round to 2 decimal places.

Diff: 2 Var: 1

Section: 6.3

Learning Objectives: Use the Fundamental Theorem to calculate definite integrals exactly.

7) Evaluate . Round to 2 decimal places.

Diff: 1 Var: 1

Section: 6.3

Learning Objectives: Use the Fundamental Theorem to calculate definite integrals exactly.

8) Evaluate . Round to 2 decimal places.

Diff: 2 Var: 1

Section: 6.3

Learning Objectives: Use the Fundamental Theorem to calculate definite integrals exactly.

9) Propellant is leaking out from the pressurized fuel tanks of the space shuttle, causing the pressure to decrease at a rate of r(t) 15 psi per second at time t in seconds. By how many psi has the pressure dropped during the first 30 seconds? Round to 2 decimal places.

Diff: 2 Var: 1

Section: 6.3

Learning Objectives: Use the Fundamental Theorem to calculate definite integrals exactly.

10) Use the Fundamental Theorem of Calculus to determine the value of b if the area under the graph of between and is 1. Assume

Diff: 2 Var: 1

Section: 6.3

Learning Objectives: Use the Fundamental Theorem to calculate definite integrals exactly.

11) A. Use the Fundamental Theorem to find for a constant

B. Take the limit of your answer to part (A) as b → ∞ to find .

A. 1 -

B. 1

Diff: 3 Var: 1

Section: 6.3

Learning Objectives: Use the Fundamental Theorem to calculate definite integrals exactly.

12) At time t hours after taking medication, the rate at which the medication is being eliminated from the body is given by r(t) = 60 mg/hr. Assuming that all of the medication is eventually eliminated, how many mg was the original dose?

Diff: 2 Var: 1

Section: 6.3

Learning Objectives: Use the Fundamental Theorem to calculate definite integrals exactly.

13) Evaluate .

A) B) C) D)

Diff: 3 Var: 1

Section: 6.3

Learning Objectives: Use the Fundamental Theorem to calculate definite integrals exactly.

14) Evaluate .

A) B) C) - D) -

Diff: 2 Var: 1

Section: 6.3

Learning Objectives: Use the Fundamental Theorem to calculate definite integrals exactly.

15) Find .

A)

B)

C) -

D) 1

E) This improper integral diverges.

Diff: 3 Var: 1

Section: 6.3

Learning Objectives: Interpret and estimate improper integrals.

16) The improper integral diverges.

Diff: 2 Var: 1

Section: 6.3

Learning Objectives: Interpret and estimate improper integrals.

17) The improper integral converges for all positive values of p.

Diff: 2 Var: 1

Section: 6.3

Learning Objectives: Interpret and estimate improper integrals.

18) The improper integral converges.

Diff: 2 Var: 1

Section: 6.3

Learning Objectives: Interpret and estimate improper integrals.

19) Compute .

A) B) -

C) D) -

Diff: 3 Var: 1

Section: 6.3

Learning Objectives: Use the Fundamental Theorem to calculate definite integrals exactly.

20) Fuel pressure in the fuel tanks of the space shuttle is decreasing at a rate of psi per second at time t in seconds. By how many total psi has the pressure decreased during the first minute? Round to 2 decimal places.

Diff: 2 Var: 1

Section: 6.3

Learning Objectives: Use the Fundamental Theorem to calculate definite integrals exactly.

21) If converges, find its value. Otherwise, enter "DNC".

Diff: 1 Var: 1

Section: 6.3

Learning Objectives: Interpret and estimate improper integrals.

22) If converges, find its value. Otherwise, enter "DNC".

Diff: 2 Var: 1

Section: 6.3

Learning Objectives: Interpret and estimate improper integrals.

23) If converges, find its value. Otherwise, enter "DNC".

Diff: 2 Var: 1

Section: 6.3

Learning Objectives: Interpret and estimate improper integrals.

6.4 Application: Consumer and Producer Surplus

1) The following figure shows the demand and supply curves for a product. Estimate the equilibrium quantity.

A) 0 B) 140 C) 250 D) 400

Diff: 1 Var: 1

Section: 6.4

Learning Objectives: Show consumer and producer surplus at equilibrium price given a graph or formula for supply and demand curves.

2) The following figure shows the demand and supply curves for a product. Estimate the consumer surplus.

A) $1125 B) $1000 C) $400 D) $875

Diff: 1 Var: 1

Section: 6.4

Learning Objectives: Show consumer and producer surplus at equilibrium price given a graph or formula for supply and demand curves.

3) The following figure shows the demand and supply curves for a product. Estimate the total gains from trade.

A) $1400 B) $2000 C) $1275 D) $2125

Diff: 2 Var: 1

Section: 6.4

Learning Objectives: Show consumer and producer surplus at equilibrium price given a graph or formula for supply and demand curves.

4) The following figure shows the demand and supply curves for a product. At an artificially imposed price of $14, what quantity will consumers buy?

A) 120 B) 150 C) 190 D) 220

Diff: 2 Var: 1

Section: 6.4

Learning Objectives: Determine the effect on consumer and producer surplus at controlled price either above or below equilibrium price.

5) The following figure shows the demand and supply curves for a product. At an artificially imposed price of $12, estimate the total gains from trade.

A) $2125 B) $2000 C) $1800 D) $2300

Diff: 2 Var: 1

Section: 6.4

Learning Objectives: Determine the effect on consumer and producer surplus at controlled price either above or below equilibrium price.

6) Supply and demand curves for a product are shown in the following figure. Estimate the equilibrium price.

Diff: 1 Var: 1

Section: 6.4

Learning Objectives: Show consumer and producer surplus at equilibrium price given a graph or formula for supply and demand curves.

7) Supply and demand curves for a product are shown in the following figure. Estimate the consumer surplus, to the nearest thousand dollars.

Diff: 1 Var: 1

Section: 6.4

Learning Objectives: Show consumer and producer surplus at equilibrium price given a graph or formula for supply and demand curves.

8) Supply and demand curves for a product are shown in the following figure. Suppose an artificially low price of $300 is imposed. Estimate the producer surplus now, to the nearest 500 dollars.

Diff: 2 Var: 1

Section: 6.4

Learning Objectives: Determine the effect on consumer and producer surplus at controlled price either above or below equilibrium price.

9) Supply and demand curves for a product are given by the equations

Demand: p = 80 - 7.15q

Supply: p = 0.2 + 10

where p is price in dollars and q is quantity. Find the equilibrium price.

Diff: 1 Var: 1

Section: 6.4

Learning Objectives: Determine the effect on consumer and producer surplus at controlled price either above or below equilibrium price.

10) Supply and demand curves for a product are given by the equations

Demand: p = 80 - 7.15q

Supply: p = 0.2 + 10

where p is price in dollars and q is quantity. Compute the producer surplus. Round to the nearest cent.

Diff: 1 Var: 1

Section: 6.4

Learning Objectives: Determine the effect on consumer and producer surplus at controlled price either above or below equilibrium price.

11) Supply and demand data are given in the following tables.

Which table shows demand?

A) The first one B) The second one

Diff: 2 Var: 1

Section: 6.4

Learning Objectives: Determine the effect on consumer and producer surplus at controlled price either above or below equilibrium price.

12) Supply and demand data are given in the following tables.

What is the equilibrium price?

Diff: 2 Var: 1

Section: 6.4

Learning Objectives: Determine the effect on consumer and producer surplus at controlled price either above or below equilibrium price.

13) Supply and demand data are given in the following tables.

Estimate the producer surplus.

Diff: 2 Var: 1

Section: 6.4

Learning Objectives: Determine the effect on consumer and producer surplus at controlled price either above or below equilibrium price.

14) The demand curve for a product has equation p = 50, and the supply curve has equation for where q is quantity and p is the price per unit. Use a calculator to find the equilibrium price and quantity, and use this information to calculate the producer surplus, to the nearest dollar.

Diff: 2 Var: 1

Section: 6.4

Learning Objectives: Determine the effect on consumer and producer surplus at controlled price either above or below equilibrium price.

15) The demand curve for a product has equation p = 50, and the supply curve has equation for where q is quantity and p is the price per unit. At an artificially high price of $27, find the quantity consumers are willing to purchase and the quantity producers are willing to supply. Use this information to calculate the consumer surplus at this price, to the nearest dollar.

Diff: 2 Var: 1

Section: 6.4

Learning Objectives: Determine the effect on consumer and producer surplus at controlled price either above or below equilibrium price.

16) The supply and demand curves for a product have equations and , respectively, with equilibrium at Which of the following is a formula for consumer surplus?

A)

B)

C)

D)

E)

Diff: 2 Var: 1

Section: 6.4

Learning Objectives: Determine the effect on consumer and producer surplus at controlled price either above or below equilibrium price.

17) The supply and demand curves for a product have equations and , respectively, with equilibrium at Which of the following is a formula for producer surplus?

A)

B)

C)

D)

E)

Diff: 2 Var: 1

Section: 6.4

Learning Objectives: Determine the effect on consumer and producer surplus at controlled price either above or below equilibrium price.

18) The supply and demand curves for a product have equations and , respectively, with equilibrium at Which of the following is a formula for total gains from trade?

A)

B)

C)

D)

E)

Diff: 2 Var: 1

Section: 6.4

Learning Objectives: Determine the effect on consumer and producer surplus at controlled price either above or below equilibrium price.

19) The supply and demand curves for a product have equations and , respectively, with equilibrium at Suppose an artificially low price of is imposed, with the resulting consumer demand of . Which of the following is a formula for the change in total gains from trade caused by the artificial price?

A) B)

C) D)

Diff: 2 Var: 1

Section: 6.4

Learning Objectives: Determine the effect on consumer and producer surplus at controlled price either above or below equilibrium price.

20) Supply and demand curves for a medical equipment product are given in the graph below.

a) Estimate the equilibrium price and quantity.

b) Estimate the consumer surplus.

c) Estimate the total gains from trade for this piece of equipment.

a) $28,000, 14 pieces of equipment

b) $96,000

c) $240,000

Diff: 1 Var: 1

Section: 6.4

Learning Objectives: Determine the effect on consumer and producer surplus at controlled price either above or below equilibrium price.

21) Supply and demand curves for an item of medical equipment are shown in the graph below. In order to compete with a new product by a rival company, the price is temporarily lowered to $20,000. What is the reduction (from equilibrium) in producer surplus that results from this artificially low price?

A) The producer surplus is reduced by $48,000.

B) The producer surplus is reduced by $59,000.

C) The producer surplus is unaffected.

D) The producer surplus is reduced by $36,000.

Diff: 1 Var: 1

Section: 6.4

Learning Objectives: Determine the effect on consumer and producer surplus at controlled price either above or below equilibrium price.

6.5 Application: Present and Future Value

1) What is the present value of an income stream of $1000 per year for 10 years with an annual interest rate of 2%, compounded continuously? Round to the nearest dollar.

Diff: 1 Var: 1

Section: 6.5

Learning Objectives: Compute the present and future values of an income stream given by a formula.

2) From the time a child is born until he is 18, a father plans to set aside $100 times the child's current age each year. Find the present value of this income stream, given an interest rate of 7% compounded continuously. Round to the nearest dollar.

Diff: 1 Var: 1

Section: 6.5

Learning Objectives: Compute the present and future values of an income stream given by a formula.

3) A. Find the present value of an income stream of $2500 per year for a period of 5 years if the interest rate is 8%. Round to the nearest dollar.

B. Find the future value of this income stream. Round to the nearest dollar.

A. $10,303

B. $15,370

Diff: 1 Var: 1

Section: 6.5

Learning Objectives: Compute the present and future values of an income stream given by a formula.

4) A consultant expects an income stream of $15,000 per year for the next 8 years.

A. Find the present value of this income stream if the interest rate is 8% per year, compounded continuously.

B. Find the future value of this income stream under the same conditions.

A. $88,633

B. $168,091

Diff: 1 Var: 1

Section: 6.5

Learning Objectives: Compute the present and future values of an income stream given by a formula.

5) At what constant, continuous annual rate should you deposit money into an account if you want to have $1,000,000 in 10 years? The account earns 5% interest, compounded continuously. Round to the nearest dollar.

Diff: 2 Var: 1

Section: 6.5

Learning Objectives: Compute the present and future values of an income stream given by a formula.

6) A lottery winner is offered a choice between

A. a lump sum of $50,000 now, or

B. $5000 per year for 15 years.

If the interest rate is 5%, compounded continuously, which is a better choice? Answer A or B.

Diff: 2 Var: 1

Section: 6.5

Learning Objectives: Compute the present and future values of an income stream given by a formula.

7) You are considering buying a salt water chlorinator for your swimming pool. The equipment costs $1300, and you estimate that you will save $275 per year with the saltwater system. Will the chlorinator pay for itself in 6 years (i.e. will the present value of the cost of the chemicals equal or exceed the cost of the chlorinator)? Assume an annual interest rate of 7%, compounded continuously. Answer "yes" or "no".

Diff: 2 Var: 1

Section: 6.5

Learning Objectives: Compute the present and future values of an income stream given by a formula.

8) A family invests in a snow cone stand that has an annual income of $13,000. If they plan to keep the stand for 10 years and save all of the income in an account earning 4.5% interest, compounded continuously, what will their total savings be?

Diff: 1 Var: 1

Section: 6.5

Learning Objectives: Compute the present and future values of an income stream given by a formula.

9) Business A predicts an income stream of 1000 dollars per year t years from now. Business B predicts an income stream of dollars per year t years from now. Assuming an annual interest rate of 4%, compounded continuously, which is worth more after 4 years? Answer "A" or "B".

Diff: 2 Var: 1

Section: 6.5

Learning Objectives: Compute the present and future values of an income stream given by a formula.

10) Business A predicts an income stream of 1000 dollars per year t years from now. Business B predicts an income stream of dollars per year t years from now. Assuming an annual interest rate of 3%, compounded continuously, which is worth more after 5 years? Answer "A" or "B".

Diff: 2 Var: 1

Section: 6.5

Learning Objectives: Compute the present and future values of an income stream given by a formula.

11) A young couple wants to start a family in five years time. They plan to add an addition to their home in four years so it is ready when they start their family. They estimate that $95,000 will be needed in four years. They can earn 7% on an investment now. If the couple makes one lump sum deposit now in order to have $95,000 in four years, how much should they deposit.

A) $71,799 B) $71,163 C) $72,616 D) $72,755

Diff: 1 Var: 1

Section: 6.5

Learning Objectives: Compute the present and future values of an income stream given by a formula.

12) A young couple wants to start a family in five years time. They plan to add an addition to their home in four years so it is ready when they start their family. They estimate that $140,000 will be needed in four years. They can earn 8% on an investment now. If the couple adds money to an investment at a continuous, constant rate for the entire four-year period, at what rate (in dollars per year) should the money be deposited in order to reach the goal of $140,000 in four years?

A) $29,698 B) $30,203 C) $28,786 D) $29,853

Diff: 1 Var: 1

Section: 6.5

Learning Objectives: Compute the present and future values of an income stream given by a formula.

13) Your company is downsizing and offers you a bonus if you retire early. You have a choice between a lump sum of $30,000 now or an income stream of $4000 per year for 10 years. You plan to use the money for a trip around the world in 10 years. You can earn interest at a continuous rate of 4%. Which option would be the better choice, and how much will you have for your trip?

Diff: 1 Var: 1

Section: 6.5

Learning Objectives: Compute the present and future values of an income stream given by a formula.

6.6 Integration by Substitution

1) Which of the following are appropriate for integration by substitution? Select all that apply.

A)

B)

C)

D)

E)

Diff: 1 Var: 1

Section: 6.6

Learning Objectives: Use a substitution to find an indefinite integral.

2) Find using integration by substitution.

A) + C B) + C

C) + C D) + 4 + C

Diff: 1 Var: 1

Section: 6.6

Learning Objectives: Use a substitution to find an indefinite integral.

3) Find using integration by substitution.

A) cos + C B) - cos + C

C) cos + C D) - cos + C

Diff: 2 Var: 1

Section: 6.6

Learning Objectives: Use a substitution to find an indefinite integral.

4) Find using integration by substitution.

A) + C B) 3y ln + C

C) ln + C D) ln + C

Diff: 2 Var: 1

Section: 6.6

Learning Objectives: Use a substitution to find an indefinite integral.

5) Find using integration by substitution.

A) + C B) + C

C) + C D) + C

Diff: 2 Var: 1

Section: 6.6

Learning Objectives: Use a substitution to find an indefinite integral.

6) Find using integration by substitution.

A) + C B) + C C) + C D) + C

Diff: 2 Var: 1

Section: 6.6

Learning Objectives: Use a substitution to find an indefinite integral.

7) Find using integration by substitution.

A) + C B) + C

C) + C D) + C

Diff: 3 Var: 1

Section: 6.6

Learning Objectives: Use a substitution to find an indefinite integral.

8) Find .

A) + C B) + C

C) + C D) + C

Diff: 1 Var: 1

Section: 6.6

Learning Objectives: Use a substitution to find an indefinite integral.

9) Find .

A) + C B) + C

C) + C D) - + C

Diff: 3 Var: 1

Section: 6.6

Learning Objectives: Use a substitution to find an indefinite integral.

10) Which of the following is equivalent to f (x) = + C?

A) B)

C) D)

Diff: 2 Var: 1

Section: 6.6

Learning Objectives: Use a substitution to find an indefinite integral.

11) Which of the following is equivalent to f (x) = ln + C?

A) B)

C) D)

Diff: 3 Var: 1

Section: 6.6

Learning Objectives: Use a substitution to find an indefinite integral.

12) = + + + C

Diff: 1 Var: 1

Section: 6.6

Learning Objectives: Use a substitution to find an indefinite integral.

13) Find .

A) 5 sin + C B) sin + C

C) -5 sin + C D) - sin + C

Diff: 1 Var: 1

Section: 6.6

Learning Objectives: Use a substitution to find an indefinite integral.

14) Evaluate .

A) - + C B) + C

C) - + C D) + C

Diff: 2 Var: 1

Section: 6.6

Learning Objectives: Use a substitution to find an indefinite integral.

15) Consider . What is the definite integral obtained after making the substitution

A) B)

C) D)

Diff: 1 Var: 1

Section: 6.6

Learning Objectives: Use a substitution to evaluate a definite integral.

16) Find .

A) + C B) + C

C) + C D) + C

Diff: 2 Var: 1

Section: 6.6

Learning Objectives: Use a substitution to find an indefinite integral.

17) Find .

A) - + C B) + C

C) 2 + C D) -2 + C

Diff: 2 Var: 1

Section: 6.6

Learning Objectives: Use a substitution to find an indefinite integral.

18) Fuel pressure in the fuel tanks of the space shuttle is decreasing at a rate of r(t) = 14 psi per second at time t in seconds. At what rate, in psi/sec, is pressure decreasing at 25 seconds? Round to 2 decimal places.

Diff: 1 Var: 1

Section: 6.6

Learning Objectives: Use a substitution to evaluate a definite integral.

19) Calculate .

A) + C B) + C

C) + C D) + C

Diff: 2 Var: 1

Section: 6.6

Learning Objectives: Use a substitution to find an indefinite integral.

6.7 Integration by Parts

1) Suppose (x) = and F(0) = 6. Find F(2) to 2 decimal places.

Diff: 1 Var: 1

Section: 6.7

Learning Objectives: Use a substitution to evaluate a definite integral.

2) The following figure is a graph of (x). Which of the following statements are correct, assuming that the domain of is [-2, 3]? Select all that apply.

A) -2 is a local maximum B) -2 is a local minimum

C) 1 is a local maximum D) 1 is a local minimum

E) 3 is a local maximum F) 3 is a local minimum

Diff: 1 Var: 1

Section: 6.7

Learning Objectives: Sketch the graph of a function given information on its derivative.

3) True or False: = - + C, where a is a constant.

Diff: 2 Var: 1

Section: 6.7

Learning Objectives: Use integration by parts to find indefinite integrals.

4) True or False: = x ln x - x + C.

Diff: 2 Var: 1

Section: 6.7

Learning Objectives: Use integration by parts to find indefinite integrals.

5) True or False: = 2(x + 1) + C.

Diff: 2 Var: 1

Section: 6.7

Learning Objectives: Use integration by parts to find indefinite integrals.

6) Use integration by parts to find .

Diff: 1 Var: 1

Section: 6.7

Learning Objectives: Use integration by parts to find indefinite integrals.

7) Use integration by parts to find .

Diff: 1 Var: 1

Section: 6.7

Learning Objectives: Use integration by parts to find indefinite integrals.

8) Use integration by parts to find .

Diff: 2 Var: 1

Section: 6.7

Learning Objectives: Use integration by parts to find indefinite integrals.

9) Use integration by parts to find . (Give the exact answer in terms of natural logs.)

Diff: 2 Var: 1

Section: 6.7

Learning Objectives: Use integration by parts to evaluate definite integrals.

10) Use integration by parts to find .

Diff: 2 Var: 1

Section: 6.7

Learning Objectives: Use integration by parts to evaluate definite integrals.

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