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# a9 - University of Toronto at Scarborough Department of...

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University of Toronto at Scarborough Department of Computer and Mathematical Sciences MATA37 Calculus II for Mathematical Sciences Summer 2007 Assignment #9 This is the last assignment. Work on the text material and the problems below in preparation for the the Final Exam, which takes place Monday, August 13, 2-5pm, Room H-215. The last tutorial in on Tuesday, July 31. The quiz there will cover material on integration at your TA’s discretion. IMPORTANT NOTE! Our course will end with Chapters 19. You only need to concern yourself with problems 1 - 4 below. We will OMIT Chapters 20, 23 and 24 and you can therefore OMIT problems 5 - 11 below. PROBLEMS: 1. Page 377-386 # 3(ix); 4(iii, x); 5(v); 6(ii, iv, v); 8(v, vi); 14; 23. 2. Determine the values of the real number p such that the improper integral R 1 1 x p dx converges. 3. For each improper integral, determine whether it converges or diverges. If the improper integral converges, evaluate it. (a) R 1 (3 x + 1) - 2 dx (b) R - 1 -∞ (2 - x ) - 1 / 2 dx (c) R -∞ xe - x 2 dx (d) R 0 ( x 2 + 3 x + 2) - 1 dx (e) R -∞ x

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