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Homework 3

Homework 3 - Garcia Ilse – Homework 3 – Due 3:00 am –...

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Unformatted text preview: Garcia, Ilse – Homework 3 – Due: Sep 11 2007, 3:00 am – Inst: Fonken 1 This print-out should have 16 questions. Multiple-choice questions may continue on the next column or page – find all choices before answering. The due time is Central time. 001 (part 1 of 3) 10 points (i) Determine the value of lim x → 2+ x- 3 x- 2 . 1. limit =- 3 2 2. none of the other answers 3. limit = ∞ 4. limit = 3 2 5. limit =-∞ correct Explanation: For 2 < x < 3 we see that x- 3 x- 2 < . On the other hand, lim x → 2+ x- 2 = 0 . Thus, by properties of limits, lim x → 2+ x- 3 x- 2 =-∞ . 002 (part 2 of 3) 10 points (ii) Determine the value of lim x → 2- x- 3 x- 2 . 1. none of the other answers 2. limit = 3 2 3. limit =- 3 2 4. limit = ∞ correct 5. limit =-∞ Explanation: For x < 2 < 3 we see that x- 3 x- 2 > . On the other hand, lim x → 2- x- 2 = 0 . Thus, by properties of limits, lim x → 2- x- 3 x- 2 = ∞ . 003 (part 3 of 3) 10 points (iii) Determine the value of lim x → 2 x- 3 x- 2 . 1. limit = 3 2 2. limit =- 3 2 3. none of the other answers correct 4. limit = ∞ 5. limit =-∞ Explanation: If lim x → 2 x- 3 x- 2 exists, then lim x → 2+ x- 3 x- 2 = lim x → 2- x- 3 x- 2 . But as parts (i) and (ii) show, lim x → 2+ x- 3 x- 2 6 = lim x → 2- x- 3 x- 2 . Consequently, lim x → 2 x- 3 x- 2 does not exist . Garcia, Ilse – Homework 3 – Due: Sep 11 2007, 3:00 am – Inst: Fonken 2 keywords: limit, left hand limit, right hand limit, rational function, 004 (part 1 of 1) 10 points Suppose that f ( x ) is defined for all x in U = (3 , 4) ∪ (4 , 5) and that lim x → 4 f ( x ) = L. Which of the following statements is then true? I) If L > 0, then f ( x ) > 0 on U . II) If f ( x ) > 0 on U , then L ≥ 0. III) If L = 0, then f ( x ) = 0 on U . 1. II only correct 2. each of I, II, III 3. II, III only 4. I, II only 5. I, III only 6. None of these Explanation: I) False: consider the function f ( x ) = 1- 2 | x- 4 | . Its graph is 2 4 6 so lim x → 4 f ( x ) = 1 . But on (3 , 7 2 ) and on ( 9 2 , 5) we see that f ( x ) < 0. II) True: if f ( x ) > 0 on U , then on U the graph of f always lies above the x-axis....
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Homework 3 - Garcia Ilse – Homework 3 – Due 3:00 am –...

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