Final Exam Problems
(Please extend sufficient space if you work on the docx version)
[10 points]
1. Use Part 1 of the Fundamental Theorem of Calculus to find the derivative of the function:
[20 points]
2. Let , where is the function whose graph is shown below.
a) Evaluate , , , , and
) On what intervals is increasing?
c) Where does have a maximum value?
d) Sketch a graph of the function
[25 points]
3. Use Part 2 of the Fundamental Theorem of Calculus to evaluate the definite integral.
a)
)
c)
d)
e)
[10 points]
4. Find the indefinite integral:
a)
)
[10 points]
5. Find the area of the region bounded by the curves: and
[10 points]
6. Find the average value of the function on the interval
[9 points]
7. A tennis ball is thrown vertically downward from a height of 54 feet with an initial velocity of 8 feet/sec.
a) What is the velocity of the ball at time ?
) What is the position of the ball at time ?
c) What is the impact velocity if it hits a 6-foot tall person on the head?
[6 points]
8. The fuel tank on a large truck has trapezoidal cross sections with dimensions (in feet) shown in the figure below. Assume that the engine is approximately 2 feet above the top of the fuel tank and that diesel fuel weighs approximately 55.6 pounds per cubic foot.
Find the work done by the fuel pump in raising a full tank of fuel to the level of the engine.
Hint: Use the fact that