# A2_2011 - 2. Spivak # 2.8, 2.12, 2.13, 3.3(i)-(iii), 3.16,...

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University of Toronto at Scarborough MAT A37H Summer 2011 Assignment # 2 You are expected to work on this assignment prior to your tutorial during the week of May 23rd. You may ask questions about this assignment in that tutorial. At the beginning of your TUTORIAL during the week of May 30th you need to submit the following homework problems. STUDY: Chapter 2 (pg 25-26), Chapters 3-4. Chapter 5 (excluding pgs 100-107). HOMEWORK PROBLEMS: 1. Prove that 2 + 12 is irrational. 2. Spivak # 3.3(iv). 3. Prove that lim x 2 x 4 - 2 x 3 + x + 3 = 5 . 4. Prove that lim x 3 x 2 + 1 1 - x = - 5 . 5. Consider the function f ( x ) = ± 2 x if x Q - 2 x if x / Q Show that lim x 0 f ( x ) = 0 . EXERCISES: You do not need to submit these questions but you should make sure that you are able to answer them;

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1. Let P ( n ) denote ”7 n - 2 n = 5 x ” for some x N . Prove P ( n ) holds n N by using the Principle of Well Ordering (PWO).
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Unformatted text preview: 2. Spivak # 2.8, 2.12, 2.13, 3.3(i)-(iii), 3.16, 3.19(i), 3.21(a)(b). 3. Let A = { 1 , 3 , 4 , 5 , 8 } and B = { 2 , 3 , 4 , 5 } . The set { (1 , 4) , (5 , 2) , (4 , 5) , (3 , 3) , (8 , 4) } denes a function from A into B . T or F 4. Find the domain of the function f ( x ) = q x-1 x +1 + 1 log 4 (4-2 x ) . 5. Prove that: (a) lim x a x = a where a R ,a &gt; . (b) lim x 1 2 x 2-3 x + 1 x-1 = 1 . (c) lim x 2 1 ( x-3) 2 = 1 . (d) lim x 3 x 3-2 x 2 + x-1 = 11 . (e) lim x x cos 6 x = 0 . (f) lim x 1 ( x 2-1) sin 1 x-1 = 0 . 6. Let f : R R be a function and let a R , R . Give a precise denition of f does not approach at a . ie. lim x a f ( x ) 6 = . Make sure to simplify/negate your denition correctly. 2...
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## This note was uploaded on 09/19/2011 for the course MATH 01 taught by Professor Katherine during the Summer '11 term at University of Toronto- Toronto.

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A2_2011 - 2. Spivak # 2.8, 2.12, 2.13, 3.3(i)-(iii), 3.16,...

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