Problem 1: Non-calculator problem so you must show all work.
If g(x) = x2 - 3x + 4 and f(x) = g’(x), then
Problem 2: Non-calculator problem so you must show all work.
If and , then
Problem 3-4: Non-calculator problems so you must show all work.
3. =4.
Problem 5:
A spherical tank contains 81.637 gallons of water at time
t = 0 minutes. For the next 6 minutes, water flows out of the tank at the rate of gallons per minute. How many gallons of water are in the tank at the end of the 6 minutes?
Show what you typed into your calculator – don’t just write an answer. Remember you should have three decimal places.
Problem 6:
The rate at which raw sewage enters a treatment tank is given by gallons per hour for
0 t 4 hours. Treated sewage is removed from the tank at the constant rate of 645 gallons per hour. The treatment tank is empty at time t = 0. How many gallons of sewage enter the containment tank during the time interval 0 t 4 hours? Round your answer to the nearest gallon.
Show what you typed into your calculator – don’t just write an answer.
Problem 7: Calculator problem. Show what you put into your calculator.
A particle moves along the x-axis so that its velocity at time t 0 is given by . What is the total distance traveled by the particle from t = 0 to t = 2? (Note – this is asking for total distance traveled, not displacement.)
Problem 8-9: Non-calculator problems so you must show all work.
8. 9.
Problem 10: Non-calculator problems so you must show all work.
A particle with velocity at any time t given by v(t) = et moves in a straight line. How far does the particle move from t = 0 to t = 2? Your answer will be in terms of e.
Problem 11: Non-calculator problem so you must show all work.
If , then k =
Problem 12-13: Non-calculator problems so you must show all work.
12.
13. If the function f has a continuous derivative on [0,c], then =
A. f(c) – f(0)B. |f(c) – f(0)|C. f(c)
D. f(x) + cE. f”(c) – f”(0)
Problem 14
The graph of f’, the derivative of f, is the line shown in the figure above. If f(0) = 5, then f(1) = ?
Problem 15
The velocity, in ft/sec, of a particle moving along the x-axis is given by the function v(t) = et + tet. What is the average velocity of the particle from time t = 0 to time
t = 3?
Show what you typed into your calculator – don’t just write an answer.
Problems 16-17 Non-Calculator Problems
16. For x > 0,
A. B. C.
D. E.
17.
A. x3 – x – 6 B. x3 – xC. 3x2 – 12D. 3x2 – 1 E. 6x – 12
Problem 18
A particle moves along a straight line so that at time t > 0 the position of the particle is given by s(t), the velocity is given by v(t), and the acceleration is given by a(t). Which of the following expressions gives the average velocity of the particle on the interval [2,8]?
A. B. C.
D. E.
Problems 19 and 20 – Calculator problems.
19. If is an antiderivative for f(x), then =
A. -0.281B. -0.102C. 0.102D. 0.260E. 0.282
20. At time t = 0 years, a forest preserve has a population of 1500 deer. If the rate of growth of the population is modeled by deer per year, what is the population at time t = 3? Show your set up and answer.