Honors AP Calculus / Mr. Hansen	Name: _______________________________
11/30/2009	Spare battery bonus (Mr. Hansen’s use only): __________

Test #5 (100 pts.): Calculator Required

1.	State, correctly, both versions of the Fundamental Theorem of Calculus. Then prove that the “derivative of an accumulator function” version, if true, would imply the truth of the other version.

2.(a)	Let , and suppose that f (.05) is given to be 2.181. Compute f (1.062) correct to 3 decimal places. Show some setup work to indicate how you obtained your answer.
(b)	Let g be any function at all, such that g is defined on and has a continuous derivative. Write an expression for g(x) if g(.05) is known to be 2.181 and knowledge of is available. Prove that your answer for g(x) works, in other words that taking the derivative gives and that g(.05) = 2.181.

3.	The deadliness of war, in number of soldiers lost per hour, fluctuates according to the “death function” D(t) = 6 cos(t/30) + 11, where t = time in hours since the start of the war. Compute the total number of soldiers who die in the first two days of the war. Give answer to the nearest number of whole people.
4.	For the function y = x^2 + 2x + 7, compute the definite integral from x = 2 to x = 2.6 several ways.
	(a) Exactly, using FTC.
	(b) With the trapezoid rule and 8 intervals (show work on reverse).
	(c) With the midpoint rule and 8 intervals (show work on reverse).
	(d) With Simpson’s Rule and 4 intervals (show work on reverse).
	(e) With a suitable weighted average of (b) and (c) that produces a Simpson’s Rule estimate (show work on reverse).
	(f) Explain why your answer in (d) is exact except for calculator rounding error.

5.	Find . Hint: Think of the arctangent.