This preview shows pages 1–3. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: Tran, Tony Homework 3 Due: Sep 11 2007, 3:00 am Inst: Samuels 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 5+ x 6 x 5 . 1. limit = correct 2. limit = 3. limit = 6 5 4. limit = 6 5 5. none of the other answers Explanation: For 5 < x < 6 we see that x 6 x 5 < . On the other hand, lim x 5+ x 5 = 0 . Thus, by properties of limits, lim x 5+ x 6 x 5 = . 002 (part 2 of 3) 10 points (ii) Determine the value of lim x 5 x 6 x 5 . 1. limit = 6 5 2. limit = correct 3. limit = 4. none of the other answers 5. limit = 6 5 Explanation: For x < 5 < 6 we see that x 6 x 5 > . On the other hand, lim x 5 x 5 = 0 . Thus, by properties of limits, lim x 5 x 6 x 5 = . 003 (part 3 of 3) 10 points (iii) Determine the value of lim x 5 x 6 x 5 . 1. limit = 2. none of the other answers correct 3. limit = 6 5 4. limit = 5. limit = 6 5 Explanation: If lim x 5 x 6 x 5 exists, then lim x 5+ x 6 x 5 = lim x 5 x 6 x 5 . But as parts (i) and (ii) show, lim x 5+ x 6 x 5 6 = lim x 5 x 6 x 5 . Consequently, lim x 5 x 6 x 5 does not exist . Tran, Tony Homework 3 Due: Sep 11 2007, 3:00 am Inst: Samuels 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. I, II only 2. II only correct 3. II, III only 4. each of I, II, III 5. None of these 6. I, 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....
View
Full
Document
This note was uploaded on 04/27/2008 for the course M 408k taught by Professor Schultz during the Fall '08 term at University of Texas at Austin.
 Fall '08
 schultz

Click to edit the document details