Honors AP Calculus / Mr. Hansen	Name: _______________________________
11/29/2012

Test #2 (100 points): Chapters 3, 4, 5, 6

General Instructions:

§ No calculator is permitted on today’s test.

§ Simplification is not required. Incorrect simplification may result in a deduction of points.

§ Final answers must be circled in order to earn full credit. Units are required when appropriate.

§ Keep your eyes on your own paper. Exceptions may result in immediate loss of your paper.

§ Show your work. Work is required for credit in each problem.

1.	If the position function of a particle is h(t) = 7 + 5t ^–1.6, where height is given in centimeters and time is given in seconds, find (a) the velocity when t = 5 seconds (b) the acceleration function
2.	Find if x and y satisfy the equation 5x^3y^7 = y^1.6.
3.	For the curve defined by 2 cos xy = x^2 – 7y + 1, find an equation of the line that is tangent at (1, 0).

4.	Let f be the function defined by f (x) = x^2 + 1 if x 1, f (x) = a(x – 2)^2 + b otherwise. Find values of the parameters a and b that make f differentiable at (1, 2).
5.	Prove that differentiability implies continuity. Provide steps and brief reasons (a word or two).

6.	The force (in pounds) required to push a slipping object varies with the distance (in feet) from the starting point. Here is a table of distances and associated forces.
		Feet	Pounds
		0	0
		0.05	120
		0.10	240
		0.15	360
		0.20	370
		0.25	330
		0.30	290
		0.35	280
		0.40	270
		0.45	270
		0.50	190
	Use Simpson’s Rule (setup only, no final numeric answer!) to compute the total work done in moving the object 6 inches. Units are required, as they are throughout this test. Use the capital letter W (for “work”) somewhere in your answer. The use of “. . .” (ellipsis) is not permitted on this problem.
7.	Explain briefly why Simpson’s Rule would not be appropriate if we had one additional data point at 0.55 feet and wanted to know the work done in pushing the object 0.55 feet.
8.	Evaluate
9.	Evaluate