a3 - 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 #3 Work on the text and lecture material and the problems below in preparation for your 3rd tutorial which takes place during the week of May 28 - June 1. Remember: you will have a quiz on assignment 2 in your 3rd tutorial also. The quiz on assignment 3 is in your 4th tutorial which takes place during the week of June 4-8. STUDY: Chapters 5 and 6 for this assignment. Chapters 7-9 for the near-future lectures. PROBLEMS: 1. Page 117-119 # 5, 6, 13, 16(a-c). 2. Assume f is continuous on R . If f ( c ) < 0 for some c R , prove there exists an open interval ( a,b ) containing c such that f ( x ) < 0 for all x ( a,b ). Formulate an analogous statement if f is positive at c . 3. Assume h is continuous on R . Give any point c R , show there exists a number K 0 and numbers a < b such that | h ( x ) | ≤ K for all x [ a,b ]. 4. Let
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This note was uploaded on 10/28/2010 for the course MATHEMATIC MATA37 taught by Professor Vadim during the Winter '08 term at University of Toronto.

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