MTH 135 Week 5 – Make up Exam #1 Name: ________________________________________ Date: _________________________ MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

1. Solve the problem.

38) How long will it take for $8400 to grow to $14.600 at an interest rate of 9.4% if the interest is compounded

continuously? Round the number of years to the nearest hundredth. 1) ______

A) 5.88 yr B) 58.81 yr C) 0.59 yr D) 0.06 yr

Use a sign chart to solve the inequality. Express answers in interval notation.

2. > 16 2) ______

A) (-4, 4 ) B) (-?, -4) ? (4, ?) C) (-4, ?) D) (4, ?)

3. Provide an appropriate response.

Given f(x + h) – f(x) = 4xh + 4h + 2 , find the slope of the tangent line at x = 4. 3) ______

A) 16 B) 8 C) 22 D) 20

4. Find the limit, if it exists.

2) Find: 4) _______

A) 0 B) – C) D) Does not exist

The graph of y = f(x) is shown. Use the graph to answer the question.

5. Is f continuous at x = -1?

5) ______

A) Yes B) No

Provide an appropriate response.

6. Find the horizontal asymptote, if any, of the given function.

f(x) = 6) _______

A) x = 2, x = -2 B) y = 3, y = -4 C) y = 1 D) None

7. Use a sign chart to solve the inequality. Express answers in interval notation.

> 0 7) ______

A) B) C) (0, ?) D)

Solve the problem.

8. Suppose that the cost C of removing p% of the pollutants from a chemical dumping site is given by

C(p) = .

Can a company afford to remove 100% of the pollutants? Explain. 8) _______

A) Yes, the cost of removing p% of the pollutants is $ 40,000, which is certainly affordable.

B) Yes, the cost of removing p% of the pollutants is $ 400, which is certainly affordable.

C) No, the cost of removing p% of the pollutants increases without bound as p approaches 100.

D) No, the cost of removing p% of the pollutants is $ 400, which is a prohibitive amount of money.

9. Find the instantaneous rate of change for the function at the value given.

Find the instantaneous rate of change for the function + 7x at x = 8. 9) ______

A) 16 B) 15 C) 120 D) 23

10. Find the instantaneous rate of change for the function f(x) = 5×2 + x at x = – 4. 10) ______

A) -41 B) -14 C) 6 D) -39

Use the graph to evaluate the indicated limit and function value or state that it does not exist.

11 Find f(x) and f(x).

11) _______

A) -1; 5 B) 5; Does not exist

C) Does not exist; does not exist D) 5; -1

12. Use the definition f'(x) = to find the derivative at x.

f(x) = 6 – 6×2 12) ______

A) 6 – 12x B) -12x C) 6 – 6x D) -12

13. f(x) = 4x – 3×3 13) ______

A) 4 – 9×2 B) 4x – 9×3 C) 4 – 3×2 D) 4x – 9×2

14. Find the equation of the tangent line to the curve when x has the given value.

Find the equation of the tangent line to the graph of the function at the given value of x.

f(x) = + 5x at x = 4 14) ______

A) y = – x + B) y = x + C) y = 13x – 16 D) y = – 39x – 80

Solve the problem.

15. Suppose an object moves along the y-axis so that its location is y = f(x) = + x at time x (y is in meters and x

is in seconds). Find the average velocity for x changing from 3 to 3 + h seconds. 15) ______

A) 7 + h m/s B) 12 + h m/s C) 7 – h m/s D) 12 – h m/s

Provide an appropriate response.

16. A spherical balloon is being inflated. Find the approximate change in volume if the radius increases from

6.1 cm to 6.3 cm. (Recall that V = ? .) 16) ______

A) 302.64 B) 148.84? C) 29.768? D) 0.976?

17. Let Find f(x). 17) _______

A) -7 B) -2 C) 5 D) Does not exist

Solve the problem.

18. An object moves along the y-axis (marked in feet) so that its position at time t (in seconds) is given by

Find the velocity at three seconds. 18) ______

A) 109 feet per second B) 192 feet per second

C) 190 feet per second D) 197 feet per second

19. The revenue (in thousands of dollars) from producing x units of an item is modeled by

Find the marginal revenue at x = 1000. 19) ______

A) $4.50 B) $4.00 C) $10,300.00 D) $104.00

Provide an appropriate response.

20. Find y’ if 20) ______

A) x B) C) 6 D) 0

21. Find f'(x) for f(x) = 2 + 6 . 21) ______

A) 2 + 6 B) 10 + 48 C) 10 + 48 D) 10 + 48

22. Find ( – ) 22) ______

A) – B) –

C) – D) –

Solve the problem.

23. If an object moves along a line so that it is at y = f(x) = 8 at time x (in seconds), find the velocity at

23) ______

A) 16 ft / s B) 160 ft/s C) 6 ft/sec D) 8 ft / s

24. Find f'(x) for f(x) = 2 + 6 . 24) ______

A) 2 + 6 B) 10 + 48 C) 10 + 48 D) 10 + 48

25. Find the equation of the tangent line at x = 2 for f(x) = 4 + x – 2 – 3 . Write the answer in the form

25) ______

A) y = -39x + 52 B) y = -43x + 60 C) y = -43x + 48 D) y = -47x + 68

26. Given f(x) = 4 and g(x) = -5, find . 26) _______

A) – B) C) D) –

27. Find f'(x) if f(x) = 9 – 5 + 10000. 27) ______

A) f'(x) = – 10x + 4000 B) f'(x) = – 10x

C) f'(x) = – 10x D) f'(x) = – 10x + 4000

28. The total cost in dollars of producing x lawn mowers is given by Find the marginal

average cost at x = 20, ‘(20) and interpret the result. 28) ______

A) -$20.33; a unit increase in production will decrease the average cost per unit by approximately $20.33 at a

production level of 20 units.

B) -$13.33; a unit increase in production will decrease the average cost per unit by approximately $13.33 at a

production level of 20 units.

C) -$1.33; a unit increase in production will decrease the average cost per unit by approximately $1.33 at a

production level of 20 units.

D) -$10.33; a unit increase in production will decrease the average cost per unit by approximately $10.33 at a

production level of 20 units.

Use -? or ? where appropriate to describe the behavior at each zero of the denominator and identify all vertical asymptotes.

29. f(x) = 29) _______

A) f(x) = ?; f(x) = -?; x = -4 is a vertical asymptote

B) f(x) = ?; f(x) = -?; x = 4 is a vertical asymptote

C) No zeros of denominator; no vertical asymptotes

D) f(x) = ?; f(x) = ?; x = 0 is a vertical asymptote

Provide an appropriate response.

30. Find t to four decimal places.

= 0.06 30) ______

A) -2.8134 B) 2.6134 C) 2.9134 D) 2.8134

31. Find: 5000 31) ______

A) 0 B) ? C) 5000 D) 1

Solve the problem.

32. A company is planning to manufacture a new blender. After conducting extensive market surveys, the

research department estimates a weekly demand of 600 blenders at a price of $50 per blender and a weekly

demand of 800 blenders at a price of $40 per blender. Assuming the demand equation is linear, use the

research department’s estimates to find the revenue equation in terms of the demand x.

32) ______

A) R(x) = 80x – 20 B) R(x) = 80x – 20

C) R(x) = 20x + D) R(x) = 80x –

33. How long will it take money to double if it is invested at compounded continuously? Round your

answer to the nearest tenth. 33) ______

A) 0.13 yr B) 13.2 yr C) 26.4 yr D) 14 yr

34. Find (x).

f(x) = 9 – 2 34) ______

A) 9x – 8 B) 9 – 4 C) 9 – 8 D) 9 – 8

35. f(x) = ln 35) ______

A) B) C) D) 5 ln

36. f(x) = ln – 8 + 2 36) ______

A) – 8x + 4x B) – 8 + 2x

C) – 8 + 4x D) – 8 + 4

37. Let f(x) =

Find f(x). 37) _______

A) 4 B) ? C) -4 D) Does not exist

38. Radioactive carbon-14 has a continuous compound rate of decay of r = -0.000124. Estimate the age of a skull

uncovered at an archaeological site if 6% of the original amount of carbon-14 is still present. (Compute

answer to the nearest year.)

38) ______

A) 22,689 yr B) 124,027 yr C) 470 yr D) 20,032 yr

39. Find the equation of the line tangent to the graph of f at the indicated value of x.

f(x) = 5 ln x; x = 1 39) ______

A) y = 5x + 5 B) y = 5x C) y = 5x – 1 D) y = 5x – 5

Solve.

40) The resale value R (in dollars) of a company car after t years is estimated to be given by

What is the rate of depreciation (in dollars per year) after 5 years? 40) ______

A) -$ 1157/yr B) -$ 15,144/yr C) -$ 1378/yr D) -$ 1641/yr

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MTH135MakeupforExam1Week5.pdf
Home>Mathematics homework help>Maaaath
MTH 135 Week 5 – Make up Exam #1 Name: ________________________________________ Date: _________________________ MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

1. Solve the problem.

38) How long will it take for $8400 to grow to $14.600 at an interest rate of 9.4% if the interest is compounded

continuously? Round the number of years to the nearest hundredth. 1) ______

A) 5.88 yr B) 58.81 yr C) 0.59 yr D) 0.06 yr

Use a sign chart to solve the inequality. Express answers in interval notation.

2. > 16 2) ______

A) (-4, 4 ) B) (-?, -4) ? (4, ?) C) (-4, ?) D) (4, ?)

3. Provide an appropriate response.

Given f(x + h) – f(x) = 4xh + 4h + 2 , find the slope of the tangent line at x = 4. 3) ______

A) 16 B) 8 C) 22 D) 20

4. Find the limit, if it exists.

2) Find: 4) _______

A) 0 B) – C) D) Does not exist

The graph of y = f(x) is shown. Use the graph to answer the question.

5. Is f continuous at x = -1?

5) ______

A) Yes B) No

Provide an appropriate response.

6. Find the horizontal asymptote, if any, of the given function.

f(x) = 6) _______

A) x = 2, x = -2 B) y = 3, y = -4 C) y = 1 D) None

7. Use a sign chart to solve the inequality. Express answers in interval notation.

> 0 7) ______

A) B) C) (0, ?) D)

Solve the problem.

8. Suppose that the cost C of removing p% of the pollutants from a chemical dumping site is given by

C(p) = .

Can a company afford to remove 100% of the pollutants? Explain. 8) _______

A) Yes, the cost of removing p% of the pollutants is $ 40,000, which is certainly affordable.

B) Yes, the cost of removing p% of the pollutants is $ 400, which is certainly affordable.

C) No, the cost of removing p% of the pollutants increases without bound as p approaches 100.

D) No, the cost of removing p% of the pollutants is $ 400, which is a prohibitive amount of money.

9. Find the instantaneous rate of change for the function at the value given.

Find the instantaneous rate of change for the function + 7x at x = 8. 9) ______

A) 16 B) 15 C) 120 D) 23

10. Find the instantaneous rate of change for the function f(x) = 5×2 + x at x = – 4. 10) ______

A) -41 B) -14 C) 6 D) -39

Use the graph to evaluate the indicated limit and function value or state that it does not exist.

11 Find f(x) and f(x).

11) _______

A) -1; 5 B) 5; Does not exist

C) Does not exist; does not exist D) 5; -1

12. Use the definition f'(x) = to find the derivative at x.

f(x) = 6 – 6×2 12) ______

A) 6 – 12x B) -12x C) 6 – 6x D) -12

13. f(x) = 4x – 3×3 13) ______

A) 4 – 9×2 B) 4x – 9×3 C) 4 – 3×2 D) 4x – 9×2

14. Find the equation of the tangent line to the curve when x has the given value.

Find the equation of the tangent line to the graph of the function at the given value of x.

f(x) = + 5x at x = 4 14) ______

A) y = – x + B) y = x + C) y = 13x – 16 D) y = – 39x – 80

Solve the problem.

15. Suppose an object moves along the y-axis so that its location is y = f(x) = + x at time x (y is in meters and x

is in seconds). Find the average velocity for x changing from 3 to 3 + h seconds. 15) ______

A) 7 + h m/s B) 12 + h m/s C) 7 – h m/s D) 12 – h m/s

Provide an appropriate response.

16. A spherical balloon is being inflated. Find the approximate change in volume if the radius increases from

6.1 cm to 6.3 cm. (Recall that V = ? .) 16) ______

A) 302.64 B) 148.84? C) 29.768? D) 0.976?

17. Let Find f(x). 17) _______

A) -7 B) -2 C) 5 D) Does not exist

Solve the problem.

18. An object moves along the y-axis (marked in feet) so that its position at time t (in seconds) is given by

Find the velocity at three seconds. 18) ______

A) 109 feet per second B) 192 feet per second

C) 190 feet per second D) 197 feet per second

19. The revenue (in thousands of dollars) from producing x units of an item is modeled by

Find the marginal revenue at x = 1000. 19) ______

A) $4.50 B) $4.00 C) $10,300.00 D) $104.00

Provide an appropriate response.

20. Find y’ if 20) ______

A) x B) C) 6 D) 0

21. Find f'(x) for f(x) = 2 + 6 . 21) ______

A) 2 + 6 B) 10 + 48 C) 10 + 48 D) 10 + 48

22. Find ( – ) 22) ______

A) – B) –

C) – D) –

Solve the problem.

23. If an object moves along a line so that it is at y = f(x) = 8 at time x (in seconds), find the velocity at

23) ______

A) 16 ft / s B) 160 ft/s C) 6 ft/sec D) 8 ft / s

24. Find f'(x) for f(x) = 2 + 6 . 24) ______

A) 2 + 6 B) 10 + 48 C) 10 + 48 D) 10 + 48

25. Find the equation of the tangent line at x = 2 for f(x) = 4 + x – 2 – 3 . Write the answer in the form

25) ______

A) y = -39x + 52 B) y = -43x + 60 C) y = -43x + 48 D) y = -47x + 68

26. Given f(x) = 4 and g(x) = -5, find . 26) _______

A) – B) C) D) –

27. Find f'(x) if f(x) = 9 – 5 + 10000. 27) ______

A) f'(x) = – 10x + 4000 B) f'(x) = – 10x

C) f'(x) = – 10x D) f'(x) = – 10x + 4000

28. The total cost in dollars of producing x lawn mowers is given by Find the marginal

average cost at x = 20, ‘(20) and interpret the result. 28) ______

A) -$20.33; a unit increase in production will decrease the average cost per unit by approximately $20.33 at a

production level of 20 units.

B) -$13.33; a unit increase in production will decrease the average cost per unit by approximately $13.33 at a

production level of 20 units.

C) -$1.33; a unit increase in production will decrease the average cost per unit by approximately $1.33 at a

production level of 20 units.

D) -$10.33; a unit increase in production will decrease the average cost per unit by approximately $10.33 at a

production level of 20 units.

Use -? or ? where appropriate to describe the behavior at each zero of the denominator and identify all vertical asymptotes.

29. f(x) = 29) _______

A) f(x) = ?; f(x) = -?; x = -4 is a vertical asymptote

B) f(x) = ?; f(x) = -?; x = 4 is a vertical asymptote

C) No zeros of denominator; no vertical asymptotes

D) f(x) = ?; f(x) = ?; x = 0 is a vertical asymptote

Provide an appropriate response.

30. Find t to four decimal places.

= 0.06 30) ______

A) -2.8134 B) 2.6134 C) 2.9134 D) 2.8134

31. Find: 5000 31) ______

A) 0 B) ? C) 5000 D) 1

Solve the problem.

32. A company is planning to manufacture a new blender. After conducting extensive market surveys, the

research department estimates a weekly demand of 600 blenders at a price of $50 per blender and a weekly

demand of 800 blenders at a price of $40 per blender. Assuming the demand equation is linear, use the

research department’s estimates to find the revenue equation in terms of the demand x.

32) ______

A) R(x) = 80x – 20 B) R(x) = 80x – 20

C) R(x) = 20x + D) R(x) = 80x –

33. How long will it take money to double if it is invested at compounded continuously? Round your

answer to the nearest tenth. 33) ______

A) 0.13 yr B) 13.2 yr C) 26.4 yr D) 14 yr

34. Find (x).

f(x) = 9 – 2 34) ______

A) 9x – 8 B) 9 – 4 C) 9 – 8 D) 9 – 8

35. f(x) = ln 35) ______

A) B) C) D) 5 ln

36. f(x) = ln – 8 + 2 36) ______

A) – 8x + 4x B) – 8 + 2x

C) – 8 + 4x D) – 8 + 4

37. Let f(x) =

Find f(x). 37) _______

A) 4 B) ? C) -4 D) Does not exist

38. Radioactive carbon-14 has a continuous compound rate of decay of r = -0.000124. Estimate the age of a skull

uncovered at an archaeological site if 6% of the original amount of carbon-14 is still present. (Compute

answer to the nearest year.)

38) ______

A) 22,689 yr B) 124,027 yr C) 470 yr D) 20,032 yr

39. Find the equation of the line tangent to the graph of f at the indicated value of x.

f(x) = 5 ln x; x = 1 39) ______

A) y = 5x + 5 B) y = 5x C) y = 5x – 1 D) y = 5x – 5

Solve.

40) The resale value R (in dollars) of a company car after t years is estimated to be given by

What is the rate of depreciation (in dollars per year) after 5 years? 40) ______

A) -$ 1157/yr B) -$ 15,144/yr C) -$ 1378/yr D) -$ 1641/yr

Applied Sciences
Architecture and Design
Biology
Business & Finance
Chemistry
Computer Science
Geography
Geology
Education
Engineering
English
Environmental science
Spanish
Government
History
Human Resource Management
Information Systems
Law
Literature
Mathematics
Nursing
Physics
Political Science
Psychology
Reading
Science
Social Science
Liberty University
New Hampshire University
Strayer University
University Of Phoenix
Walden University
Home
Homework Answers
Blog
Archive
Tags
Reviews
Contact
twitterfacebook
Copyright © 2022 SweetStudy.com