Well Justified - Calculus - Exam, Exams of Calculus

Download Well Justified - Calculus - Exam and more Exams Calculus in PDF only on Docsity! Name: ___________________________ Mathematics 106 Final Exam April 9, 2002 Problem Possible Actual 1 14 2 10 3 12 4 12 5 16 6 12 7 12 8 12 Total 100 You must show all work to receive credit. Calculators are permitted. Give exact answers (ln 5, e2) unless requested otherwise. 1. Evaluate each of the following. a) ∫ dxxx )cos( 32 b) ∫ dxxx )cos( 35 c) ∫ ∞ − 0 10 dxxe x 2. Give a well-justified argument for whether each integral below converges or diverges. You may take for granted any facts about the convergence of ∫ 1 0 1 dx x p and ∫ ∞ 1 1 dx x p that we have proved in class. a) ∫ ∞ + + 1 10 34 13 45 dx x xx b) ∫ + 1 0 85 2 dx xx x