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a4 - 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 #4 Work on the text material and the problems below in preparation for your 4th tutorial, which takes place during the week of June 4 - 8. Remember: there is a quiz on Assignment 3 in that tutorial. The quiz on Assignment 4 takes place in the 5th tutorial which is during the week of June 11 - 15. STUDY: Chapters 6-8 for this assignment and Chapters 9-11 for the near-future lectures. PROBLEMS: 1. Page 118-119 # 7; 10 (b). 2. Page 127-130 # 1 (i, iii); 3; 8; 10; 14 (a, b); 19 (a). 3. Page 137-139 # 1 (i, iii, iv); 12; 13. 4. Assume φ is continuous on a closed, bounded interval [ a, b ]. The image of [ a, b ] under φ is the set φ ([ a, b ]) = { φ ( x ) | x [ a, b ] } . Prove that φ ([ a, b ]) is a closed, bounded interval. 5. Give an example of a function ψ and a bounded, open interval ( a, b ) such that ψ is continuous on ( a, b ) but ψ (( a, b )) is an unbounded, open interval. Give an example of a function ψ that is continuous on R but for which ψ ( R ) is a bounded, open interval.
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