hw5 - EECS 203 Homework 5 Solutions Section 3.2 1(E 2abd a...

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EECS 203: Homework 5 Solutions Section 3.2 1. (E) 2abd a) Yes since 17x + 11 ≤ 17x + x = 18x ≤ 18x 2 for all x ≥ 11 b) Yes since x 2 + 1000 ≤ x 2 + x 2 = 2x 2 for all x ≥ 32. d) No since x 4 /2 ≤ Cx 2 gives x 2 /2 ≤ C for all x, which cannot be true since we can always find a value of x beyond which this becomes false. 2. (E) 6 (x 3 + 2x)/(2x + 1) ≤ (x 3 + 2x 3 )/(2x) = (3/2)x 2 for all x ≥ 1 3. (E) 14acd a) No since x 3 ≤ Cx 2 gives x ≤ C for all x beyond some specific value, which cannot be true since we can always find an x beyond which C becomes smaller. c) Yes since x 3 ≤ x 2 + x 3 for all x. That is C = 1, k = 0. d) Yes since x 3 ≤ x 2 + x 4 for all x. That is C = 1, k = 0. 4. (E) 24ab a) x ≤ 3x + 7 for all x. On the other hand 3x + 7 ≤ 4x for all x ≥ 7. That is C = 4, k = 7. b) x 2 ≤ 2x 2 + x – 7 for x > 2. On the other hand 2x 2 + x – 7 ≤ 3x 2 for all x ≥ 1. That is C = 3, k = 1. 5. (E) 26
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This note was uploaded on 01/28/2010 for the course EECS 203 taught by Professor Yaoyunshi during the Spring '07 term at University of Michigan.

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hw5 - EECS 203 Homework 5 Solutions Section 3.2 1(E 2abd a...

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