a1 - 2 Pages 27-35 1(ii(You may freely use the summation...

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University of Toronto at Scarborough Department of Computer and Mathematical Sciences MATA37 Calculus II for Mathematical Sciences Summer 2007 Assignment #1 Work on the text material, current lectures and the problems below in preparation for your 1st tutorial which takes place during the week of May 14-18. There is no quiz in the 1st tutorial. You will have a quiz on this assignment or related concepts/materials at your TA’s discretion in your 2nd tutorial which takes place during the week of May 21-25. STUDY: Chapters 1-5. Omit pages 75-89. PROBLEMS: 1. Pages 13-18 # 3(ii) (only use axioms P1-P9); 4(vi), (xiii); 5(i) (only use the deﬁnition at the top of page 10); 11(iv); 12(iv), (vi); 20; 21.
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Unformatted text preview: 2. Pages 27-35 # 1(ii) (You may freely use the summation formulas on pages 22 and 23); 5; 12(a); 14(b). 3. Page 48-53 # 1(i), (ii); 2(i), (ii); 3(v); 9(a), (b); 13; 16(a) (use the PMI); 19(i). 4. Pages 68-69 # 1(i), (iii); 2(a); 3(v); 4(i). 5. Show that any interval of the form ( a,b ) where a,b ∈ R and a < b can be written in the form ( m-δ,m + δ ) for some m,δ ∈ R where δ > 0. (The second interval is said to be symmetric with center m and radius δ ) 6. Prove these two inequalities: (a) q x 2 + y 2 ≤ x + y where x,y ∈ R and x,y ≥ 0. (b) | x y + y x | ≥ 2 for all non-zero real numbers x and y ....
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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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