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Unformatted text preview: Granillo, Yvette – Homework 3 – Due: Sep 15 2005, 3:00 am – Inst: Edward Odell 1 This printout should have 25 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 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 twosided 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.
 Spring '08
 schultz

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