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Unformatted text preview: Jolley, Garrett – Homework 3 – Due: Sep 11 2007, 3:00 am – Inst: R Heitmann 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 → 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 xaxis....
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This note was uploaded on 10/29/2008 for the course M 408k taught by Professor Schultz during the Spring '08 term at University of Texas.
 Spring '08
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