MATH 205 Midterm: MATH 205 Louisville Practice Exam 3 111114 Solutions
Document Summary
Practice exam #3 solutions: (12 points) answer the following questions: (a) (6 points) determine a region whose area is lim n n. The area of a region under a curve f (x) from x = a to x = b is known to be lim n n. Xi=1 (cid:18) b a n (cid:19) f (cid:18)a + A n i(cid:19) , which bears a similarity except in details to the expression given. We must therefore nd expressions to stand in for a, b, and f (x) to make these expressions equivalent. Taking the most na ve decomposition of these equivalent expressions, we nd that. A n i(cid:19) = ln 2 + The rst equation clearly establishes that b a = 5; substituting this knowledge into the second equation, we nd that our correspondences become: A = 5 i(cid:19) = ln 2 +
