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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) = 5x2 + 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 - 6x2 12) ______

A) 6 - 12x B) -12x C) 6 - 6x D) -12

13. f(x) = 4x - 3x3 13) ______

A) 4 - 9x2 B) 4x - 9x3 C) 4 - 3x2 D) 4x - 9x2

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 = π .) 16) ______

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

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