# hw3 - Granillo Yvette – Homework 3 – Due 3:00 am –...

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Unformatted text preview: Granillo, Yvette – Homework 3 – Due: Sep 15 2005, 3:00 am – Inst: Edward Odell 1 This print-out should have 25 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 1) 10 points Suppose lim x → 5 f ( x ) = 4 . Consider the following statements: A. Range of f contains 4. B. As f ( x ) approaches 4, x approaches 5. C. f is defined on ( a, b ) for some a < 5 < b . Which of these statements are true without further restrictions on f ? 1. all of them 2. none of them correct 3. B only 4. C only 5. A and B only 6. A only 7. A and C only 8. B and C only Explanation: A. Not True: ( f ( x ) need only AP- PROACH 4). B. Not True: ( f ( x ) approaches 4 AS x approaches 5). C. Not true: ( f ( x ) need not be defined at x = 5). keywords: Stewart5e, True/False, definition limit 002 (part 1 of 1) 10 points Below is the graph of a function f . 2 4 6- 2- 4- 6 2 4 6 8- 2- 4 Use the graph to determine lim x → 4 f ( x ) . 1. limit = 8 2. limit = 6 3. limit does not exist correct 4. limit = 18 5. limit = 9 Explanation: From the graph it is clear the f has a left hand limit at x = 4 which is equal to 8; and a right hand limit which is equal to- 3. Since the two numbers do not coincide, the limit does not exist . keywords: Stewart5e, limit, graph, limit at jump discontinuity 003 (part 1 of 1) 10 points Below is the graph of a function f . Granillo, Yvette – Homework 3 – Due: Sep 15 2005, 3:00 am – Inst: Edward Odell 2 2 4- 2- 4 2 4- 2- 4 Use the graph to determine lim x → 4 f ( x ). 1. does not exist 2. limit = 1 3. limit =- 2 correct 4. limit =- 1 5. limit = 0 Explanation: From the graph it is clear that the limit lim x → 4- f ( x ) =- 2 , from the left and the limit lim x → 4+ f ( x ) =- 2 , from the right exist and coincide in value. Thus the two-sided lim x → 4 f ( x ) =- 2 . keywords: Stewart5e, limit, graph, limit at removable discontinuity 004 (part 1 of 1) 10 points Consider the function f ( x ) = 1- x, x <- 1 x,- 1 ≤ x < 3 ( x- 1) 2 , x ≥ 3 . Find all the values of a for which the limit lim x → a f ( x ) exists, expressing your answer in interval no- tation. 1. (-∞ , ∞ ) 2. (-∞ ,- 1) ∪ (- 1 , ∞ ) 3. (-∞ ,- 1) ∪ (- 1 , 3) ∪ (3 , ∞ ) correct 4. (-∞ ,- 1] ∪ [3 , ∞ ) 5. (-∞ , 3) ∪ (3 , ∞ ) Explanation: The graph of f is a straight line on (-∞ ,- 1), so lim x → a f ( x ) exists (and = f ( a )) for all a in (-∞ ,- 1). Similarly, the graph of f on (- 1 , 3) is a straight line, so lim x → a f ( x ) exists (and = f ( a )) for all a in (- 1 , 3). On (3 , ∞ ), however, the graph of f is a parabola, so lim x → a f ( x ) still exists (and = f ( a )) for all a in (3 , ∞ )....
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## This test prep was uploaded on 04/16/2008 for the course M 408k taught by Professor Schultz during the Spring '08 term at University of Texas.

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hw3 - Granillo Yvette – Homework 3 – Due 3:00 am –...

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