Honors AP Calculus / Mr. Hansen	Name: _______________________________
11/24/2009	Spare battery bonus (Mr. Hansen’s use only): __________

Test #5 CFU: Calculator Required

1.	State both versions of the Fundamental Theorem of Calculus, and prove that each implies the other.

2.	Let , and suppose that f (2) is given to be 3.184. Compute f (2.2) correct to 3 decimal places by using (a) your calculator, (b) Simpson’s Rule (showing work).
(c)	For any unknown differentiable function g whose derivative is known, assume that g(2) is also known. Write an expression for g(2.2).

3.	The difficulty of being a student, in stress units per day, is given by D(t) = 5 cos(t/30) + 11, where t = time in school days since the start of the school year. Compute the total difficulty of a year at STA (152 days).
4.	Explain why the trapezoid rule always overestimates , no matter how many intervals are used. Phrase your answer in terms of the second derivative of the integrand.

5.	Find . Hint: Think of the arctangent.