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Unformatted text preview: Villarreal, Natalie Homework 3 Due: Sep 11 2007, 3:00 am Inst: Louiza Fouli 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 6 x 2 . 1. limit = 3 2. limit = 3 3. limit = correct 4. limit = 5. none of the other answers Explanation: For 2 < x < 6 we see that x 6 x 2 < . On the other hand, lim x 2+ x 2 = 0 . Thus, by properties of limits, lim x 2+ x 6 x 2 = . 002 (part 2 of 3) 10 points (ii) Determine the value of lim x 2 x 6 x 2 . 1. limit = 3 2. limit = 3. limit = correct 4. none of the other answers 5. limit = 3 Explanation: For x < 2 < 6 we see that x 6 x 2 > . On the other hand, lim x 2 x 2 = 0 . Thus, by properties of limits, lim x 2 x 6 x 2 = . 003 (part 3 of 3) 10 points (iii) Determine the value of lim x 2 x 6 x 2 . 1. limit = 3 2. none of the other answers correct 3. limit = 3 4. limit = 5. limit = Explanation: If lim x 2 x 6 x 2 exists, then lim x 2+ x 6 x 2 = lim x 2 x 6 x 2 . But as parts (i) and (ii) show, lim x 2+ x 6 x 2 6 = lim x 2 x 6 x 2 . Consequently, lim x 2 x 6 x 2 does not exist . Villarreal, Natalie Homework 3 Due: Sep 11 2007, 3:00 am Inst: Louiza Fouli 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 = (1 , 2) (2 , 3) and that lim x 2 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. None of these 3. each of I, II, III 4. I, III only 5. I, II only 6. II, III only Explanation: I) False: consider the function f ( x ) = 1 2  x 2  . Its graph is 2 4 6 so lim x 2 f ( x ) = 1 . But on (1 , 3 2 ) and on ( 5 2 , 3) 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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 Fall '09
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