HW3 - Jolley, Garrett Homework 3 Due: Sep 11 2007, 3:00 am...

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Unformatted text preview: Jolley, Garrett Homework 3 Due: Sep 11 2007, 3:00 am Inst: R Heitmann 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 4+ x- 8 x- 4 . 1. limit = 2. limit =- 2 3. none of the other answers 4. limit =- correct 5. limit = 2 Explanation: For 4 < x < 8 we see that x- 8 x- 4 < . On the other hand, lim x 4+ x- 4 = 0 . Thus, by properties of limits, lim x 4+ x- 8 x- 4 =- . 002 (part 2 of 3) 10 points (ii) Determine the value of lim x 4- x- 8 x- 4 . 1. limit = correct 2. limit =- 2 3. none of the other answers 4. limit =- 5. limit = 2 Explanation: For x < 4 < 8 we see that x- 8 x- 4 > . On the other hand, lim x 4- x- 4 = 0 . Thus, by properties of limits, lim x 4- x- 8 x- 4 = . 003 (part 3 of 3) 10 points (iii) Determine the value of lim x 4 x- 8 x- 4 . 1. limit = 2. limit = 2 3. limit =- 4. limit =- 2 5. none of the other answers correct Explanation: If lim x 4 x- 8 x- 4 exists, then lim x 4+ x- 8 x- 4 = lim x 4- x- 8 x- 4 . But as parts (i) and (ii) show, lim x 4+ x- 8 x- 4 6 = lim x 4- x- 8 x- 4 . Consequently, lim x 4 x- 8 x- 4 does not exist . Jolley, Garrett Homework 3 Due: Sep 11 2007, 3:00 am Inst: R Heitmann 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 = (5 , 6) (6 , 7) and that lim x 6 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, III only 2. I, II only 3. each of I, II, III 4. II only correct 5. I, III only 6. None of these Explanation: I) False: consider the function f ( x ) = 1- 2 | x- 6 | . Its graph is 2 4 6 so lim x 6 f ( x ) = 1 . But on (5 , 11 2 ) and on ( 13 2 , 7) 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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HW3 - Jolley, Garrett Homework 3 Due: Sep 11 2007, 3:00 am...

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