• Author / Uploaded
• Ricardo Alberto

• Categories
• Tangente
• Geometría
• Conceptos matemáticos
• Análisis
• Objetos matemáticos

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a. 0, 2, 6 b. 2, 0, 6 c. 2, 2, 6 d. 2, 0, -2 e. 0, 1, -2

2. Suppose that the population of a colony of bacteria is growing exponentially. At the start of an experiment, there are 4000 bacteria. Two hours later there are 4600 bacteria. How long will it take the colony to reach 8200 bacteria? : * a. 10.3 hours b. 11.9 hours c. 12.3 hours d. 13.4 hours e. 14.1 hours

3.: *

a. i. only b. ii. only c. iii. only d. ii. and iii. e. None of these are true.

4.: *

a. x = 2 b. x = 4 c. x = -3, x = 4 d. x = 3/2 e. There are no vertical asymptotes.

5.: *

Choice a.

Choice b. Choice c. Choice d. Choice e.

6.: *

a. 3 b. 9 c. -9 d. √3 e. - √3

7. The height in meters of a projectile after t seconds is given by h(t) = -16t2 + 96t. Find the average velocity of the projectile on the interval [1,3]: * a. 24 m/s b. 28 m/s c. 30 m/s d. 32 m/s e. 34 m/s

8.: *

a. f(x) = x2 b. f(x) = x2 - 2x + 1 c. f(x) = x2 - 4x + 4 d. f(x) = 2x2 - 2

9.: *

a. 0 b. -(1/81) c. 1/81 d. -(1/9) e. 1/9 f. The limit does not exist.

10.: *

a. ε b. ε/2

c. ε/4 d. ε/6 e. ε/8

11.: *

Choice a. Choice b. Choice c. Choice d. Choice e.

12.: *

a. 2 b. 3

c. 4 d. 6 e. 12

13.: *

a. 50 b. 60 c. 70 d. 80 e. 90

14.: *

a. 2 b. 4 c. 5 d. 6 e. 8

15.: *

a. 1 b. -2 c. 1, -2 d. The function is continuous everywhere.

16. The function f shown in the graph has a removable discontinuity at which value of x?: *

a. 0 b. 1 c. 5 d. 6 e. None of the above

17.: *

a. 3x2 + 3xh + h2 b. 3x2h + 3x2h2 + h3 c. 2x3 + 2xh d. 3x2 e. h2

18.: *

a. -1 b. 1 c. -2 d. 2

19.: *

a. 0.1 b. 0.2 c. 0.3 d. 0.4 e. 0.5

20. If an equation of the tangent line to the curve y = f(x) at the point α = 2 is y = 4x - 5, find f(2), f'(2): * a. 3, 2 b. 2, 3 c. 4, 2 d. 2, 4 e. 3, 4 f. 4, 3

21. Use differentials to estimate the amount of paint needed to apply a coat of paint 0.18 cm thick to a hemispherical dome with diameter 60 meters.: * a. 2.52π b. 3.24π c. 3.82π d. 2.28π e. 4.11π

22. Gravel is being dumped from a conveyor belt at a rate of 35 ft3/min and its forms a pile in the shape of a cone whose base and height are always equal. How fast is the height of the pile increasing when the height is 15 feet high?: * a. 0.27 ft/min b. 1.24 ft/min

c. 0.14 ft/min d. 0.20 ft/min e. 0.60 ft/min

23. How many points of inflection are on the graph of f(x) = 18x3 + 5x2 - 12x 17?: * a. 1 b. 2 c. 3 d. 4 e. 5

24.: *

a. x - y = -17 b. x - y = -12 c. x - y = -13 d. x - y = -15 e. x - y = -4

25.: *

Choice a. Choice b. Choice c. Choice d.

26.: *

a. 1/4

b. 1/2 c. -(1/4) d. -(1/2) e. 2

27.: *

Choice a. Choice b. Choice c. Choice d.

28. Use Newton’s Method to find the fourth approximation x 4 the solution of the equation cosx = x when x1 = 1: * a. 0.851 b. 0.513 c. 0.750 d. 0.638

e. 0.739

29.: *

Choice a. Choice b. Choice c. Choice d.

30.: *

Choice a.

Choice b. Choice c. Choice d. Choice e.

31.: *

a. 3 b. 1 c. 0 d. -(1/2) e. -2

32.: *

a. 0.539 b. 0.792 c. 0.817 d. 0.693

33. Which of the following is true?: *

a. d is an antiderivative of c b. c is an antiderivative of d c. a is an antiderivative of c d. c is an antiderivative of a e. d is an antiderivative of b f. b is an antiderivative of d

34.: *

Choice a.

Choice b. Choice c. Choice d. Choice e. Choice f.

35. If a force of 20 N is required to extend a spring 4 cm longer than its natural length, how much work is done to extend it that far?: * a. 100 J b. 80 J c. 60 J d. 40 J e. 20 J

36. Find the volume of the solid formed by rotating the region bounded by the curves y = x2, y = 1 about the line y = 2: *

Choice a.

Choice b. Choice c. Choice d. Choice e.

37.: *

Choice a. Choice b. Choice c. Choice d. Choice e.

38.: *

a. 0 b. 1 c. -∞ d. ∞ e. Does not exist

39.: *

Choice a. Choice b. Choice c.

Choice d. Choice e.

40.: *

Choice a. Choice b. Choice c. Choice d. Choice e.

41. Solve the differential equation: 7yyt = 5x: * a. 5x2 - 7y2 = C b. 5x2 + 7y2 = C c. 7x2 - 5y2 = C d. 7x2 + 5y2 = C

42. A curve passes through the point (4,2) and has the property that the slope of the curve at every point P is three times the y-coordinate P. What is the equation of the curve?: * a. y = 2e3x+12 b. y = 2ex-12 c. y = 2e3x-4 d. y = 2e3x-12

43. Eliminate the parameter to find a Cartesian equation of the curve. x = et - 1, y = e2t: * a. y = ln(x+1) b. y = (x+1)2 c. y = e2x+1 d. y = (x-1)2

44.: *

Choice a. Choice b.

Choice c. Choice d.

45.: *

a. A ≥ B b. A ≤ B c. A < B d. A > B e. A = B

46.: *

a. 1/3 b. 1/2 c. 2/3 d. 1 e. 3/2

47.: *

a. p < 0 b. p > 0 c. p < -1 d. p > -1 e. p < 1 f. p > 1

48.: *

a. converges absolutely b. converges conditionally c. diverges

49.: *

a. 5 b. 10

c. 15 d. 20 e. 25

50.: *

Choice a. Choice b. Choice c. Choice d. Choice e.