Exam Questions Accumulated Change The Definite Integral Ch5

Applied Calculus, 7e (Hughes-Hallett)

Chapter 5 Accumulated Change: The Definite Integral

5.1 Distance and Accumulated Change

1) The rate of pollution pouring into a lake is measured every 10 days, with results in the following table. About how many tons of pollution have entered the lake during the first 40 days?

Diff: 1 Var: 1

Section: 5.1

Learning Objectives: Estimate the total change given information about a rate of change.

2) Consider a sports car which accelerates from 0 ft/sec to 85 ft/sec in 5 seconds The car's velocity is given in the following table. What is the lower bound for the number of feet the car travels in 5 seconds?

Diff: 2 Var: 1

Section: 5.1

Learning Objectives: Estimate the total change given information about a rate of change.

3) Consider a sports car which accelerates from 0 ft/sec to 88 ft/sec in 5 seconds The car's velocity is given in the following table. Over which time interval in the average acceleration the smallest?

A) The last

B) The fourth

C) The third

D) The second

E) The first

Diff: 2 Var: 1

Section: 5.1

Learning Objectives: Estimate the total change given information about a rate of change.

4) The flow rate of water in a mountain stream due to spring runoff is given in the following table. Give your best estimate (average of upper and lower limit) of how many cubic meters of water flowed through from 6:00 pm to midnight.

Diff: 1 Var: 1

Section: 5.1

Learning Objectives: Estimate the total change given information about a rate of change.

5) The graph below shows the velocity of an object (in meters/second). Find an upper bound for the number of meters traveled from t = 0 to t = 4 seconds.

Diff: 1 Var: 1

Section: 5.1

Learning Objectives: Estimate the total change given information about a rate of change.

6) The following figure shows the graph of the velocity, v, of an object (in meters/sec). If the graph were shifted up 2 units, how would the distance traveled between and change?

A) It would increase by 2 meters.

B) It would decrease by 2 meters.

C) It would increase by 12 meters.

D) It would decrease by 12 meters.

E) It would remain the same.

Diff: 1 Var: 1

Section: 5.1

Learning Objectives: Estimate the total change given information about a rate of change.

7) A car is observed to have the following velocities at times t = 0, 2, 4, 6:

Give an upper estimate for the number of feet the car traveled in first 6 seconds.

Diff: 1 Var: 1

Section: 5.1

Learning Objectives: Estimate the total change given information about a rate of change.

8) Two cars start at the same time and travel in the same direction along a straight road. The following figure gives the velocity, v, of each car as a function of time, t. Which car traveled for the longer time?

A) Car A B) Car B

Diff: 1 Var: 1

Section: 5.1

Learning Objectives: Estimate the total change given information about a rate of change.

9) A new factory worker is put to work assembling gadgets. He is fairly slow at first, but over a period of days gets much faster. His employer constructs the following table to evaluate his progress over the first 20 days he is on the job. Give a lower estimate for the number of gadgets the worker assembled the first 10 days on the job.

Diff: 2 Var: 1

Section: 5.1

Learning Objectives: Estimate the total change given information about a rate of change.

10) Your velocity, in meters per second, is given by v(t) = + 2, where t is time in seconds. Estimate your distance traveled over the first 6 seconds.

A) 88 meters B) 94 meters C) 100 meters D) 106 meters

Diff: 2 Var: 1

Section: 5.1

Learning Objectives: Estimate the total change given information about a rate of change.

11) The following figure shows the rate of change of enrollment for a community college. Estimate the total change in enrollment over the first 8 years.

A) 3200 students B) 3600 students

C) 4000 students D) 4200 students

Diff: 2 Var: 1

Section: 5.1

Learning Objectives: Estimate the total change given information about a rate of change.

12) The balance in an investment account increases at a rate of R = 2000 dollars per year, where t is time in years since 2000. Make a table of values for R and use it to give an upper estimate for the total change in the value of the account between 2000 and 2005.

A) $10,636 B) $10,711 C) $10,786 D) $10,861

Diff: 2 Var: 1

Section: 5.1

Learning Objectives: Estimate the total change given information about a rate of change.

13) If a function is concave up, then the left-hand Riemann sums are always less than the right-hand Riemann sums with the same subdivisions, over the same intervals.

Diff: 1 Var: 1

Section: 5.1

Learning Objectives: Understand left- and right-hand sums.

14) Water is flowing into a container at an increasing rate, as shown in the following table. Give an upper estimate for the total number of gallons of water in the container after 30 minutes.

Diff: 1 Var: 1

Section: 5.1

Learning Objectives: Estimate the total change given information about a rate of change.

5.2 The Definite Integral

1) At time t, in seconds, the velocity v, in miles per hour, of a car is given by for Use to estimate how many miles were traveled during this time (average left- and right-hand sums).

Diff: 2 Var: 1

Section: 5.2

Learning Objectives: Estimate a definite integral from a table, graph, or formula.

2) At time t, in seconds, the velocity v, in feet per second, of a car is given by for A second car travels exactly 20 feet per second faster than the first car. How much greater will the left- and right-hand estimates for the distance traveled by the second car be that the left- and right-hand estimates for the distance traveled by the first car?

Diff: 2 Var: 1

Section: 5.2

Learning Objectives: Estimate a definite integral from a table, graph, or formula.

3) At time t, in seconds, your velocity, v, in meters per second, is given by for Use to estimate how many meters you traveled during this time.

Diff: 2 Var: 1

Section: 5.2

Learning Objectives: Estimate a definite integral from a table, graph, or formula.

4) At time t, in seconds, your velocity, v, in meters per second, is given by for Use to estimate how many meters you traveled during this time.

Diff: 2 Var: 1

Section: 5.2

Learning Objectives: Estimate a definite integral from a table, graph, or formula.

5) Use a calculator to estimate . Round your answer to 2 decimal places.

Diff: 1 Var: 1

Section: 5.2

Learning Objectives: Evaluate a definite integral using technology.

6) Use a calculator to evaluate . Round your answer to 2 decimal places.

Diff: 1 Var: 1

Section: 5.2

Learning Objectives: Evaluate a definite integral using technology.

7) Use a calculator to evaluate . Round your answer to 2 decimal places.

Diff: 2 Var: 1

Section: 5.2

Learning Objectives: Evaluate a definite integral using technology.

8) Use the following graph to estimate using the right Riemann sum with three terms.

Diff: 2 Var: 1

Section: 5.2

Learning Objectives: Estimate a definite integral from a table, graph, or formula.

9) Which of the following is the best approximation for , where f is shown in the following figure?

A) 300 B) 1000 C) 4500 D) 6575

Diff: 2 Var: 1

Section: 5.2

Learning Objectives: Estimate a definite integral from a table, graph, or formula.

10) Given the following graph of f , which is the best approximation for ?

A) 51,000 B) 78,750 C) 84,500 D) 100,000

Diff: 2 Var: 1

Section: 5.2

Learning Objectives: Estimate a definite integral from a table, graph, or formula.

11) Consider the graph of the function f (x) = shown in the following figure.

A. Approximate by using a right-hand sum with 3 subdivisions. Round to 2 decimal places.

B. Is your answer to part (A) a lower or an upper estimate?

A. 0.63

B. lower

Diff: 2 Var: 1

Section: 5.2

Learning Objectives: Estimate a definite integral from a table, graph, or formula.

12) You plan to approximate the definite integral by Riemann sums. Which Riemann sum will be larger, the right or the left?

Diff: 2 Var: 1

Section: 5.2

Learning Objectives: Estimate a definite integral from a table, graph, or formula.

13) Consider the function f (x) = ln x, as shown in the following figure. Taking △ x = 0.5, find the upper sum estimate for . Round to 3 decimal places.

Diff: 2 Var: 1

Section: 5.2

Learning Objectives: Estimate a definite integral from a table, graph, or formula.

14) A. Find a 4-term right Riemann sum approximation for the integral . Round to 1 decimal place.

B. Is your answer in part (A) an underestimate or an overestimate?

Part A: 69.4

Part B: overestimate

Diff: 3 Var: 1

Section: 5.2

Learning Objectives: Estimate a definite integral from a table, graph, or formula.

15) Using the following figure, calculate the value of the left-hand Riemann sum for the function f on the interval using

Diff: 2 Var: 1

Section: 5.2

Learning Objectives: Estimate a definite integral from a table, graph, or formula.

16) Use the following table to estimate using

Diff: 2 Var: 1

Section: 5.2

Learning Objectives: Estimate a definite integral from a table, graph, or formula.

17) The following table gives the rate r(t), in cubic centimeters, that air is leaking from a balloon t seconds after it is inflated. Estimate .

A) 192.5 cubic centimeters B) 49 cubic centimeters

C) 245 cubic centimeters D) 75.5 cubic centimeters

Diff: 1 Var: 1

Section: 5.2

Learning Objectives: Estimate a definite integral from a table, graph, or formula.

18) Use the following figure to estimate (average left- and right-hand sums).

Diff: 1 Var: 1

Section: 5.2

Learning Objectives: Estimate a definite integral from a table, graph, or formula.

19) Data for a function G is given in the following table. Estimate (to 3 decimal places). Average upper and lower sums.

Diff: 2 Var: 1

Section: 5.2

Learning Objectives: Estimate a definite integral from a table, graph, or formula.

20) An air conditioning unit is switched on in an 80°F room. The room is cooling off at a rate of r(t) = 2 degrees F per minute, with t in minutes after the unit was turned on. Set up an appropriate integral and evaluate it with a calculator to find the temperature of the room after 10 minutes. Round to the nearest degree.

Diff: 2 Var: 1

Section: 5.2

Learning Objectives: Evaluate a definite integral using technology.

21) If = 6, = 2, and = 12, find the value of .

Diff: 1 Var: 1

Section: 5.2

Learning Objectives: Estimate a definite integral from a table, graph, or formula.

22) If = 10, = 4, and = 14, find the value of .

Diff: 1 Var: 1

Section: 5.2

Learning Objectives: Estimate a definite integral from a table, graph, or formula.

23) If = 6, = 3, and = 12, find the value of .

Diff: 1 Var: 1

Section: 5.2

Learning Objectives: Estimate a definite integral from a table, graph, or formula.

24) Given the graph:

Estimate the value of to three decimal places.

Diff: 3 Var: 1

Section: 5.2

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

5.3 The Definite Integral as Area

1) Find (x) for .

A) + 2 B) - C) D)

Diff: 1 Var: 1

Section: 5.3

Learning Objectives: Use a definite integral to find the area between two curves.

2) Find the area included between the curves y = and y = , from x = 1 to x = 5. Round to 2 decimal places.

Diff: 3 Var: 1

Section: 5.3

Learning Objectives: Use a definite integral to find the area between two curves.

3) In the following graph, does appear to be positive, negative, or zero?

Diff: 1 Var: 1

Section: 5.3

Learning Objectives: Understand a definite integral as signed area: area above the x-axis minus area below the x-axis.

4) Use the following table to estimate the area between f (x) and the x-axis on the interval

A) 3 B) 8 C) 22 D) 36

Diff: 2 Var: 1

Section: 5.3

Learning Objectives: Understand a definite integral as signed area: area above the x-axis minus area below the x-axis.

5) Your rich eccentric friend has hired you to cover his back yard with grass and patio stone. If the southwest corner of his yard is taken as the origin, with the x-axis pointing eastward and distances measured in feet, then the boundaries of the yard are the lines and The border between grass and stone is with grass covering all of the yard south of the curve. This border also bounds one side of the pool, the other side of the pool being surrounded by the curve All of the rest of the yard is to be covered by stone. Estimate, to the nearest square yard, the area of the stone.

The area of f(x) from 0-100 is 8500

The area of the pool from 20-60 is 1043

The area of the grass from 0-100 is 4254

f(x)-pool-grass= area of the stone

Diff: 3 Var: 1

Section: 5.3

Learning Objectives: Use a definite integral to find the area between two curves.

6)

A car is moving along a straight road from A to B, starting from A at time Below is the velocity plotted against time. How many kilometers away from A is the car at time

Diff: 2 Var: 1

Section: 5.3

Learning Objectives: Understand a definite integral as signed area: area above the x-axis minus area below the x-axis.

7) If the upper estimate of the area of a region bounded by the curve in the following figure, the horizontal axis, and the vertical lines and is 15, what is the upper estimate if the graph is shifted up 1 unit?

Diff: 2 Var: 1

Section: 5.3

Learning Objectives: Understand a definite integral as signed area: area above the x-axis minus area below the x-axis.

8) Estimate the area above the curve y = cos x and below y = 1 for 0 ≤ x ≤ π/2. Round to 2 decimal places.

Diff: 2 Var: 1

Section: 5.3

Learning Objectives: Use a definite integral to find the area between two curves.

9) Estimate the area of the region bounded by y = cos x , x = -π/2, and x = 0. Round to 2 decimal places.

Diff: 1 Var: 1

Section: 5.3

Learning Objectives: Use a definite integral to find the area between two curves.

10) Estimate the area of the region under the curve y = - + 6 and above the x-axis for Round to 2 decimal places.

Diff: 2 Var: 1

Section: 5.3

Learning Objectives: Use a definite integral to find the area between two curves.

11) Estimate the area of the region under the curve y = sin(x/2) for . Round to 2 decimal places.

Diff: 2 Var: 1

Section: 5.3

Learning Objectives: Use a definite integral to find the area between two curves.

12) Suppose F(x) = 3 sin x + x + 6. Find the total area bounded by F(x), x = 0, and Round to 1 decimal place.

Diff: 2 Var: 1

Section: 5.3

Learning Objectives: Use a definite integral to find the area between two curves.

13) Use an integral to find the area under the graph of y = 3 + 5 for

A) 7454.45 B) 7438.15 C) 7474.45 D) 7458.15

Diff: 1 Var: 1

Section: 5.3

Learning Objectives: Use a definite integral to find the area between two curves.

14) The upper half of the ellipse below has equation y = . Find the area in the first quadrant between the ellipse and the line Give your answer to two decimal places.

A) 1.57 B) 2.57 C) 3.14 D) 1.14

Diff: 2 Var: 1

Section: 5.3

Learning Objectives: Use a definite integral to find the area between two curves.

15) = .

Diff: 2 Var: 1

Section: 5.3

Learning Objectives: Use a definite integral to find the area between two curves.

16) If = 0 and f is continuous, then f must have at least one zero between a and b (assume a ≠ b).

Diff: 1 Var: 1

Section: 5.3

Learning Objectives: Understand a definite integral as signed area: area above the x-axis minus area below the x-axis.

17) Use the following figure to find the value of .

Diff: 2 Var: 1

Section: 5.3

Learning Objectives: Understand a definite integral as signed area: area above the x-axis minus area below the x-axis.

18) Use the following figure to find the value of .

Diff: 2 Var: 1

Section: 5.3

Learning Objectives: Understand a definite integral as signed area: area above the x-axis minus area below the x-axis.

19) Suppose f (t) is given by the following graph. If F(x) = , what is F(5)?

Diff: 2 Var: 1

Section: 5.3

Learning Objectives: Understand a definite integral as signed area: area above the x-axis minus area below the x-axis.

5.4 Interpretations of the Definite Integral

1) What are the units of if t is measured in and f is in hours?

A) km/hr B) km C) km/ D) km ∙ hr

Diff: 1 Var: 1

Section: 5.4

Learning Objectives: Interpret the definite integral of rate of change as total change.

2) A large ice cube is melting at a rate of r = f (t) per minute, where t is time in minutes. If is the volume of the ice cube at time minutes, which one of the following expresses the volume of the ice cube after 4 hours?

A) - B) -

C) D) +

Diff: 2 Var: 1

Section: 5.4

Learning Objectives: Use definite integrals to determine values of a quantity given an initial value and a rate of change.

3) A stamp collector has 5000 stamps in his collection on January 1, 2005, and is collecting more stamps at a rate of stamps per week, where t is time in weeks since January 1, 2005. Which of the following expresses the number of stamps in his collection at the end of 2005?

A) 5000 + B) 5000

C) 5000 D) 5000 +

Diff: 2 Var: 1

Section: 5.4

Learning Objectives: Use definite integrals to determine values of a quantity given an initial value and a rate of change.

4) Sales of a new product are increasing at a rate of 300 units per month, where t is time in months since the product was introduced. How many units were sold the first 4 months since the product was introduced? Set up an integral and use a calculator to evaluate it to the nearest whole unit.

Diff: 2 Var: 1

Section: 5.4

Learning Objectives: Interpret the definite integral of rate of change as total change.

5) Equal numbers of two different species of ground squirrels are introduced into an area at time with t in years. They have the growth rates shown in the following figure. Which species will have a larger population after 12 years?

A) Species A B) Species B

Diff: 1 Var: 1

Section: 5.4

Learning Objectives: Interpret the definite integral of rate of change as total change.

6) A shop is open from 9 a.m.-7 p.m. The function r(t) graphed below gives the rate at which customers arrive (in people/hour) at time t. Suppose that the salespeople can serve customers at a rate of 60 people per hour.

A. People have to start waiting in line before being served at about _____ o'clock.

B. The number of people in line when the line is the longest is about _____.

A. 12

B. 80

Diff: 2 Var: 1

Section: 5.4

Learning Objectives: Interpret the definite integral of rate of change as total change.

7) The Ethnic food line at the Cougar Eat can serve customers at the rate of about 30 per hour. From 10 a.m. until 4 p.m. one day, the rate R at which customers entered then line was about customers per hour at t hours past 10 a.m. About what time did a waiting line form?

A) 11:15 a.m. B) 11:00 a.m. C) 11:30 a.m. D) 11:45 a.m.

Diff: 2 Var: 1

Section: 5.4

Learning Objectives: Interpret the definite integral of rate of change as total change.

8) The Ethnic food line at the Cougar Eat can serve customers at the rate of about 25 per hour. From 10 a.m. until 4 p.m. one day, the rate R at which customers entered then line was about customers per hour at t hours past 10 a.m. About when was the waiting line the longest?

A) 2:30 p.m. B) 3:00 p.m. C) 5:45 p.m. D) 2:15 p.m.

Diff: 2 Var: 1

Section: 5.4

Learning Objectives: Interpret the definite integral of rate of change as total change.

9) The Ethnic food line at the Cougar Eat can serve customers at the rate of about 25 per hour. From 10 a.m. until 4 p.m. one day, the rate R at which customers entered then line was about customers per hour at t hours past 10 a.m. About how many customers were served between 10 a.m. and 4 p.m. that day? Round to the nearest whole number.

Diff: 2 Var: 1

Section: 5.4

Learning Objectives: Interpret the definite integral of rate of change as total change.

10) After a foreign substance is introduced into the blood, the rate at which antibodies are made is given by r(t) = thousands of antibodies per minute, where time t is measured in minutes and If there are no antibodies in the blood at how many antibodies are there after 3 minutes? Round to the nearest whole number.

Diff: 2 Var: 1

Section: 5.4

Learning Objectives: Interpret the definite integral of rate of change as total change.

11) The rate of growth of the net worth of a company is given by dollars per year t years after its formation in 2005. How much did it increase in value between 2005 and 2015?

Diff: 2 Var: 1

Section: 5.4

Learning Objectives: Interpret the definite integral of rate of change as total change.

12) A reagent is cooling in a laboratory instrument. Explain in words what means if F(t) is the temperature of the reagent in degrees Fahrenheit and t is time in minutes.

Diff: 2 Var: 1

Section: 5.4

Learning Objectives: Interpret the definite integral of rate of change as total change.

13) The table below gives the average rate of monthly U.S. field production of crude oil for each decade from the 1920s through the 2000s (based on estimates calculated from the U.S. Energy Information Administration). Use this data to estimate the total U.S. field production from the 1920s to the 2000s. Note that there are 120 months in a decade. Production is given in millions of barrels per month.

A) 188,160,000,000 barrels B) 94,050,000,000 barrels

C) 221,352,000,000 barrels D) 72,350,000,000 barrels

Diff: 2 Var: 1

Section: 5.4

Learning Objectives: Use definite integrals to determine values of a quantity given an initial value and a rate of change.

14) A large scale commercial bakery makes cream filling for snack cakes. The bakery puts a new machine into production. The machine ramps up gradually, increasing cream filling production at a rate of 260 pounds per day over the first week. How many pounds of cream filling does the new machine make during the first week of production?

A) 4331 B) 210 C) 1473 D) 4764

Diff: 2 Var: 1

Section: 5.4

Learning Objectives: Interpret the definite integral of rate of change as total change.

15) On a recently discovered planetoid, acceleration due to gravity is 5 feet/ . While building a research habitat, a hammer is dropped from the top of a tower and hits the ground in 22 seconds. Because the hammer is dropped, its initial velocity is 0. Use a graph of the velocity function to determine the height of the tower.

A) 1210 feet B) 2420 feet C) 968 feet D) 1452 feet

Diff: 2 Var: 1

Section: 5.4

Learning Objectives: Interpret the definite integral of rate of change as total change.

16) According to the European Journal of Clinical Pharmacology, the half-life of the ACE inhibitor lisinopril increases from 12 hours in people with normal kidney function to 24 hours in people with mild kidney failure. A group of patients takes a 5-mg dose of lisinopril at 6 a.m. The rate that lisinopril decreases in the bloodstream is given by for normal kidney function and for impaired kidney function.

After 8 hours, what is the difference of the amount of lisinopril in the bloodstream between a person with normal kidney function and a person with impaired kidney function?

Diff: 2 Var: 1

Section: 5.4

Learning Objectives: Use definite integrals to determine values of a quantity given an initial value and a rate of change.

17) A water line made of PVC decays and eventually breaks. The rate that water flows into the street from the break is given by the function r(t) = , in gallons per hour. Use a calculator or graph to determine how many gallons of water have been lost from the water line break after 15 hours.

A) 85.0 gallons B) 215 gallons

C) 93.5 gallons D) 112.5 gallons

Diff: 2 Var: 1

Section: 5.4

Learning Objectives: Interpret the definite integral of rate of change as total change.

18) The following table gives the rate, in cubic centimeters, that air is leaking from a balloon t seconds after it is inflated. Let r(t) be that rate. What is the meaning of ?

A) The rate in cubic centimeters per second that air is leaking out of the balloon after 16 seconds.

B) The total number of cubic centimeters of air that have leaked out of the balloon after 16 seconds.

C) The number of seconds it takes for 16 cubic centimeters of air to leak out of the balloon.

D) The number of seconds it takes for the rate air is leaking out of the balloon to be 16 cubic centimeters per minute.

Diff: 2 Var: 1

Section: 5.4

Learning Objectives: Interpret the definite integral of rate of change as total change.

19) The following figure shows the rate of growth of two cities, with (t) being the growth of City A after t years and (t) being the growth of City B after t years. If the two cities have the same population at t = 0, arrange the following values in order from smallest to largest by placing a "1" by the smallest, a "2" by the next smallest, and so forth.

A. 1

B. 2

C. 4

D. 3

Diff: 2 Var: 1

Section: 5.4

Learning Objectives: Use definite integrals to determine values of a quantity given an initial value and a rate of change.

20) Below is a graph of the rate r in arrivals per minute at which students line up for breakfast. The first people arrive at 6:50 am and the line opens at 7:00 a.m. The line serves students at a constant rate of 20 students per minute. Estimate the length of the line at 7:10.

A) 240 B) 340 C) 440 D) 540

Diff: 2 Var: 1

Section: 5.4

Learning Objectives: Use definite integrals to determine values of a quantity given an initial value and a rate of change.

21) Below is a graph of the rate r in arrivals per minute at which students line up for breakfast. The first people arrive at 6:50 a.m. and the line opens at 7:00 a.m. The line serves students at a constant rate of 20 students per minute. Estimate the rate at which the line is growing in length at

A) 3 people per minute B) 4 people per minute

C) 8 people per minute D) 24 people per minute

Diff: 2 Var: 1

Section: 5.4

Learning Objectives: Use definite integrals to determine values of a quantity given an initial value and a rate of change.

22) Below is a graph of the rate r in arrivals per minute at which students line up for breakfast. The first people arrive at 6:50 a.m. and the line opens at 7:00 a.m. The line serves students at a constant rate of 20 students per minute. Estimate the length of time a person who arrives at has to stand in line.

A) 5.5 minutes B) 7.5 minutes C) 11.5 minutes D) 15.5 minutes

Diff: 2 Var: 1

Section: 5.4

Learning Objectives: Use definite integrals to determine values of a quantity given an initial value and a rate of change.

23) Below is a graph of the rate r in arrivals per minute at which students line up for breakfast. The first people arrive at 6:50 a.m. and the line opens at 7:00 a.m. The line serves students at a constant rate of 20 students per minute. Estimate the time at which the line disappears.

A) 7:10 a.m. or earlier B) 7:20 a.m.

C) 7:30 a.m. D) 7:40 a.m. or later

Diff: 2 Var: 1

Section: 5.4

Learning Objectives: Use definite integrals to determine values of a quantity given an initial value and a rate of change.

5.5 Total Change and the Fundamental Theorem of Calculus

1) If the velocity function v(t) is measured in feet per second and t gives time in seconds, what are the units of measurement for ?

A) feet B) feet/second C) feet/second2 D) seconds/foot

Diff: 1 Var: 1

Section: 5.5

Learning Objectives: Apply the fundamental theorem of calculus to analyze features of a function given information about the function's derivative.

2) The marginal cost function for a manufacturing company is given by dollars per box, where q is the number of boxes manufactured. If find the total cost of manufacturing 10 boxes. Round to the nearest dollar.

Diff: 1 Var: 1

Section: 5.5

Learning Objectives: Apply the fundamental theorem of calculus to analyze features of a function given information about the function's derivative.

3) The marginal cost in dollars per unit of producing q units is given in the following table. Estimate the total variable cost to produce 25 units.

Diff: 1 Var: 1

Section: 5.5

Learning Objectives: Apply the fundamental theorem of calculus to analyze features of a function given information about the function's derivative.

4) Suppose F(0) = 0 and (x) = 2x - 2. Use a calculator to calculate F(1).

Diff: 2 Var: 1

Section: 5.5

Learning Objectives: Apply the fundamental theorem of calculus to analyze features of a function given information about the function's derivative.

5) The graph of (x) is shown in the following figure. Given that find f (10).

Diff: 1 Var: 1

Section: 5.5

Learning Objectives: Apply the fundamental theorem of calculus to analyze features of a function given information about the function's derivative.

6) The graph of f is shown in the following figure. Find F(3) if (x) and F(0) = 0.

Diff: 2 Var: 1

Section: 5.5

Learning Objectives: Apply the fundamental theorem of calculus to analyze features of a function given information about the function's derivative.

7) If r(t) represents the rate at which a country's debt is growing, then the increase in its debt between 2015 and 2020 is given by

A)

B) r(2020) - r(1980)

C)

D)

E)

Diff: 2 Var: 1

Section: 5.5

Learning Objectives: Apply the fundamental theorem of calculus to analyze features of a function given information about the function's derivative.

8) The graph of is shown below. If f is increasing at x = -1, which of the following must be true? Select all that apply.

A) (2) = (4) B) (4) > (-1)

C) (4) > 0 D) f (5) = f (6)

Diff: 2 Var: 1

Section: 5.5

Learning Objectives: Apply the fundamental theorem of calculus to analyze features of a function given information about the function's derivative.

9) If (t) = 2t is a production rate, measured in items per hour, then how many items were produced from hour 2 to hour 4?

Diff: 1 Var: 1

Section: 5.5

Learning Objectives: Apply the fundamental theorem of calculus to analyze features of a function given information about the function's derivative.

10) A local business produces souvenirs for the tourist trade. The business has fixed costs of $6 thousand, and it costs an additional $9.93 thousand in variable costs to produce 10 thousand souvenirs. A consultant told the business that their marginal cost function is dollars per thousand souvenirs. What will it cost to increase their production to 26 thousand souvenirs?

A) $7021 B) $6868 C) $2651 D) $6181

Diff: 2 Var: 1

Section: 5.5

Learning Objectives: Apply the fundamental theorem of calculus to analyze features of a function given information about the function's derivative.

11) The graph below shows a marginal cost function, (q) $ per item. If the fixed cost is $750, estimate the total cost of producing 250 items.

A) $2700 B) $1800 C) $1530 D) $2950

Diff: 2 Var: 1

Section: 5.5

Learning Objectives: Apply the fundamental theorem of calculus to analyze features of a function given information about the function's derivative.

12) The marginal cost function of producing a particular product is given by where q is quantity. If the fixed costs are $4000, what is the total cost to produce 10 items?

Diff: 2 Var: 1

Section: 5.5

Learning Objectives: Apply the fundamental theorem of calculus to analyze features of a function given information about the function's derivative.

13) The marginal cost function of producing a particular product is given by where q is the number of items produced. If the fixed costs are $5000 and the items are sold for $600 each, what is the break-even point?

Diff: 2 Var: 1

Section: 5.5

Learning Objectives: Apply the fundamental theorem of calculus to analyze features of a function given information about the function's derivative.

5.6 Average Value

1) There are no questions for Section 5.6.

Diff: 1 Var: 1

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