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a7 - 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 #7 Work on the text material and the problems below in preparation for your tutorial on Tuesday, July 17. You will have a quiz on this assignment 7 (only up to and including Chapter 11) or any of the material covered in assignment 6. STUDY: Chapters 11, 13, 14, and 19 for this assignment. Omit Chapters 12, 13-15, and 18. We will not rigorously cover the theory of integration in Chapter 13, but you should read through that material a few times anyway. It may also be useful to read about integration in Stewart’s Calculus book (as used in MATA30). Chapters 5 - 7 are appropriate there too. In Spivak’s book, study Newton’s method on page 457 and in Stewart’s book read through Section 4.9. PROBLEMS: 1. Page 202-212 # 4(a), 19, 26, 27, 32, 37, 41, 44, 49, 50, 60. 2. Let I be an interval. If a differentiable function f is strictly increasing on I , prove that f 0 ( x ) 0 for all x I . Show by an example that we cannot generally replace
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