Calc Help
MATH 140 Final Exam FormC NAME_______________________________
Professor: Dr. J. Beyers
INSTRUCTIONS
· The exam is worth 100 points. There are 26 problems (each worth 3.85 points).
· You may use a graphing calculator for this final exam.
· Please write your answer choices on this cover sheet and don’t forget to double check your solutions and answer choices before handing in your final exam.
· You must show your work to receive full credit on this exam. If you do not show your work, you may earn only partial or no credit at the discretion of the professor.
· Best of luck!
ANSWER CHOICES
22
1) _____
2) _____
3) _____
4) _____
5) _ see solution_
6) _____
7) _____
8) _____
9) _____
10) _____
11) _____
12) _____
13) _____
14) _____
15) _____
16) _____
17) _ see graph_
18) _____
19) _____
20) _____
21) _____
22) _____
23) _____
24) _____
25) _____
26) _____
1. Find the domain of the function
1) ______
(A)
(B)
(C)
(D)
(E) none of the above
2. According to the Center for Disease Control and Prevention, Table 1 shows the growth rate of the deadly Ebola Virus and the number of deaths in a small city whose initial population was 120,000 would result from the Ebola virus if left untreated after weeks.
Table 1
|
(weeks) |
(infected) |
|
0 |
5714 |
|
0.5 |
11486 |
|
1 |
21968 |
|
1.5 |
38610 |
|
2 |
60128 |
|
2.5 |
81613 |
|
3 |
98185 |
|
3.5 |
108602 |
|
4 |
114332 |
|
4.5 |
117254 |
|
5 |
118687 |
|
5.5 |
119376 |
|
6 |
119705 |
Use the data to estimate the average growth rate of the disease from week 2 to week 4.
Use the data to estimate the growth rate of the disease on week 4.
2) ______
(A) 8,652 people/week; 27,102 people/week
(B) 54,204 people/week; 8,652 people/week
(C) 27,102 people/week; 8,652 people/week
(D) 27,102; 11,460 people/week
(E) none of the above
3. Use the graph in Figure 2 to find each of the following, provided it exists. If it does not exist, explain why.
Figure 2
3a) ______
3b) ______
3c) _____
4. Suppose represents the limiting value of the following limit expression. Find using the limit principles for infinite limits (You must show all your work to receive full credit; no short cuts ):
(A)
(B)
(C)
(D)
(E) none of the above
4) ______
5. Let . Use the Intermediate Value Theorem to show there is a zero of the polynomial in the interval (2, 3).
5) ______
6. Find the derivative of the function
6) ______
(B)
(C)
(D)
(E) none of the above
7. True or False (If your answer is true, explain your reasoning; if your answer is false give a counterexample).
If is continuous on , then
7) ______
8. The graphs of , , and are shown. Identify which of the three graphs (, , ) is , , and . Explain your reasoning.
8) ______
= _______ = _______ = _______
9. The graph of a function is shown. Which graph is an antiderivative of and why?
9) ______
(A) Graph
(B) Graph
(C) Graph
(D) Graph
(E) none of the above
10. Find if
10) ______
11. A water tank has the shape of an inverted circular cone with base radius and height . If water is being pumped into the tank at a rate of , find the rate at which the water level is rising when the water is deep. (Hint: )
11) ______
(A) 0.14
(B) 0.28
(C) 2.38
(D) 16.75
(E) none of the above
12. Suppose and for all values of . How large can possibly be?
12) ______
(A) 3
(B) 5
(C) 7
(D) 9
(E) none of the above
13. Evaluate
13) ______
(A) 1/3
(B) -2/3
(C) 2
(D) 3
(E) none of the above
14. The cost to manufacture computers per day is modeled by the following equation
14) ______
The average cost is defined to be the total cost divided by the quantity produced. How fast is changing if the current production rate is 2000 computers per day and is increasing at the rate of 200 units per day?
(A) Increasing by $1.01 per day
(B) Decreasing by $1.01 per day
(C) Increasing by $125.01 per day
(D) Decreasing by $125.01 per day
(E) none of the above
15. Engineers use innovative designs to improve the ability of buildings to withstand earthquakes. For example, the San Francisco International Airport uses giant steel ball bearings built into each of the 267 columns (see Figure below) which support the weight of the airport. Each ball bearing measures 5 feet in diameter with a maximum error of 0.01 feet. What is the maximum error for this diameter in computing the volume of this ball bearing?
15) ______
Building Support Column
Base
Ball Bearing
(A) 0.785 ft3 (B) 0.685 ft3 (C) 0.575 ft3 (D) 0.365 ft3 (E) None of the above
16. Sand falling from a hopper at 10 ft3/s forms a conical sand pile whose radius is always equal to its height. How fast is the radius increasing when the radius is 5 ft?
16) ______
(A) 5 ft/sec
(B) 10 ft/sec
(C) 2/5 ft/sec
(D) not enough information
(E) none of the above
17. Sketch the graph of the function, indicating all critical points and inflection points. Apply the second derivative test at each critical point. Show the correct concave structure and indicate the behavior of as , for .
17) ______
18. An aquarium has a square base made of slate costing 8¢/in2 and four glass sides costing
3 ¢/in2. The volume of the aquarium is to be 36,000 in3. Find the dimensions of the least expensive such aquarium.
18) ______
(A) l = 30 inches; w = 30 inches; h = 40 inches
(B) l = 20 inches; w = 20 inches; h = 90 inches
(C) l = 30 inches; w = 40 inches; h = 30 inches
(D) not enough information
(E) none of the above
19. Find the open intervals on the x-axis on which the function is increasing and those on which it is decreasing.
19) ______
(A) is increasing on ; is decreasing .
(B) is decreasing on ; is increasing on .
(C) is increasing on .
(D) is increasing on ; is decreasing on .
(E) none of the above
20. Show that the function satisfies the hypotheses of the mean value theorem on the interval . Find all numbers in the interval that satisfy the conclusion of that theorem.
20) ______
(A) is continuous on ; is continuous on ;
(B) is continuous on ; is continuous on ;
(C) is continuous on ; is continuous on ;
(D) does not satisfy the Mean Value Theorem
(E) none of the above
21. Evaluate:
21) ______
(A) 14 (B) 16 (C) 50/3 (D) not possible (E) none of the above
22. A stone is dropped from the top of a building 960 ft high. What will its impact velocity be? (Note: You may ignore air resistance.)
22) ______
23. Evaluate:
23) ______
(A) 0 (B) 1/2 (C) 1 (D) -1 (E) none of the above