University of Toronto at ScarboroughDepartment of Computer and Mathematical SciencesMATA37Calculus II for Mathematical SciencesSummer 2007Assignment #7Work 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 ofthe 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 throughthat material a few times anyway.It may also be useful to read about integration in Stewart’sCalculus 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. LetIbe an interval.If a differentiable functionfis strictly increasing onI◦, prove thatf0(x)≥0 for allx∈I◦. Show by an example that we cannot generally replace
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