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# a5 - 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 #5 Work on the text material and the problems below in preparation for your 5th tutorial on Tuesday, June 12. Remember that there is a quiz on assignment 4 in that tutorial. The quiz on assignment 5 is in your 6th tutorial which is on Tuesday, June 19. This is the week of our Midterm Test (which is on Saturday, June 23, 2-4pm, in room H-215). STUDY: Chapters 8-9 for this assignment. Chapters 10-11 for future assignments and lectures. PROBLEMS: 1. Page 129 # 17, 18(a). 2. Page 137 # 1(viii), 2(a) (What is this problem really about?). 3. Let A and B be non-empty, bounded subsets of R . Define AB = { ab : a A, b B } . Determine with proof whether inf ( AB ) = inf ( A ) inf ( B ). 4. Page 161 # 1, 2, 3, 14, 15(a). 5. Define a function f on all of R by f ( x ) = x 2 if x is rational and f ( x ) = - x 2 if x is irrational. Draw a good picture of the graph of y = f ( x ). Determine with proof the points where f is differentiable. 6. Use the definition of derivative to calculate f 0 ( x ) for the function f ( x ) = x 1 / 3 . Compare the domain of

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