math

MTH 135 Make-up Exam for Week 7 exam – Given Week 9

Name___________________________________ Date: _____________________________

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Find the integral.

1) 1) _______

A) 9 - + 6x + C B) - + 6x + C

C) - + 6x + C D) 9 - + 6x + C

2) 2) _______

A) B)

C) D)

3) 3) _______

A) B)

C) - 3 + C D)

4) 4) _______

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

5) dx 5) _______

A) + C B) 2 + C

C) + C D) - + C

Solve the problem.

6) The rate of expenditure for maintenance of a particular machine is given by M'(x) = 12x , where x is time

measured in years. Total maintenance costs through the second year are $105. Find the total maintenance function.

6) _______

A) M(x) = 12 - 3 B) M(x) = 4 - 93

C) M(x) = 4 - 3 D) M(x) = 12 - 93

Provide an appropriate response.

7) Find the general solution for the differential equation y' = 5e3x 7) _______

A) e3x + C B) 15e3x + C C) 5e3x + C D) e3x + C

8) Find the particular solution for the differential equation 8) _______

A) B) y = ln + ln 2 + 3

C) y = ln - ln 2 + 3 D) y = ln

Match the differential equation with the appropriate slope field.

9) = 9) _______

A)

B)

C)

D)

Provide an appropriate response.

10) Graph the following example of unlimited growth: y = 450 , 0 ≤ t ≤ 12, 0 ≤ y ≤ 4500.

10) ______

A)

B)

C)

D)

Solve the problem.

11) Find the amount A in an account (to the nearest dollar) after 5 years if and

11) ______

A) $1000 B) $1100 C) $919 D) $1200

Provide an appropriate response.

12) Divide the interval [0, 8] into four equal subintervals and draw in the corresponding right rectangles.

12) ______

A)

B)

C)

D)

13) Given that find the definite integral

13) ______

A) B) - 6 C) D)

14) Given and use properties of definite integrals to evaluate

14) ______

A) 54 B) 13 C) 18 D) 24

Evaluate the integral.

15)

(Round to three decimal places.) 15) ______

A) 1.778 B) 1.040 C) 1.199 D) 2.398

16) 16) ______

A) 52.5 B) 34 C) 58 D) 76

17) dx 17) ______

A) 18 B) 42 C) 72 D) 36

Provide an appropriate response.

18) Find the average value of the function y = 2 over the interval [- 2, 2]. 18) ______

A) B) C) 0 D)

19) Find the average value of the function y = over the interval [ 0, 3]. Express an exact answer in terms of e.

19) ______

A) B) C) 1 - D)

Solve the problem.

20) A drug is injected into the bloodstream of a patient through her right arm. The concentration of the drug, C(t) (in

milligrams per cubic centimeter), in the blood stream of the left arm t hours after the injection is given by

What is the average concentration of the drug in the bloodstream of the left arm during the first two hours after the

injection? 20) ______

A) 0.121 milligrams per cubic centimeter B) 0.241 milligrams per cubic centimeter

C) 0.344 milligrams per cubic centimeter D) 0.060 milligrams per cubic centimeter

21) A population of bacteria grows at a rate of P'(t) = 12 where t is time in hours. Determine how much the population

increases from to Round your answer to two decimal places. 21) ______

A) 470.06 B) 229.03 C) 235.03 D) 241.03

Evaluate the integral.

22) dx 22) ______

A) B) C) D) 625

Provide an appropriate response.

23) Given and find 23) ______

A) 28 B) 26 C) 2 D) 30

Approximate the area under the graph of f(x) and above the x-axis using n rectangles.

24) f(x) = + 2; interval [0, 5]; n = 5; compute 24) ______

A) 40 B) 65 C) 32 D) 66