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Unformatted text preview: Garcia, Ilse Homework 3 Due: Sep 11 2007, 3:00 am Inst: Fonken 1 This printout should have 16 questions. Multiplechoice 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 xaxis....
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This note was uploaded on 02/22/2009 for the course M 58365 taught by Professor Gilbert during the Spring '08 term at University of Texas at Austin.
 Spring '08
 Gilbert
 Calculus

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