MATH 103 Final: MATH 103 UPenn 103Final2012Awans Exam
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Answers provided on the last page: suppose that f and g are integrable and that f x dx. ), inventor, military engineer, physicist, and the greatest mathematician of classical times in the western world, discovered that area under a parabolic arch is two-thirds the base times the height. Let h = height and b = base. Use calculus to find the area and verify archimedes" discovery for the parabola y (cid:6) 2 x whose graph is given to the right. given that h. 24e: 2, 4, 6, 8, 12, 16. 0: find the area of the shaded region y x= y = Spring 2102: for what values of a m and does the function f x (cid:12) (cid:13) (cid:14) (cid:13) (cid:15) Satisfy the hypotheses of the mean value theorem on the interval [ ]0, 2 : suppose that f x. 2 x for all x and that f . Find f ( )2 : let f x x.
