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Unformatted text preview: Version 100 EXAM 1 Radin (58280) 1 This printout should have 20 questions. Multiplechoice questions may continue on the next column or page find all choices before answering. 001 10.0 points A tank holds 1000 gallons of water, which drains from the bottom of the tank in half an hour. The values in the table t (min) 5 10 15 20 25 30 V (gal) 720 480 289 190 23 show the volume, V ( t ), of water remaining in the tank (in gallons) after t minutes. If P is the point (15 , V (15)) on the graph of V as a function of time t , find the slope of the secant line PQ when Q = (25 , V (25)). 1. slope = 53 . 2 2. slope = 19 . 1 3. slope = 43 . 1 4. slope = 9 . 9 5. slope = 26 . 6 correct Explanation: When P = (15 , V (15)) , Q = (25 , V (25)) the slope of the secant line PQ is given by rise run = V (25) V (15) 25 15 . From the table of values, therefore, we see that slope = 23 289 25 15 = 26 . 6 . 002 10.0 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 does not exist correct 2. limit = 9 3. limit = 8 4. limit = 5 5. limit = 7 Explanation: From the graph it is clear the f has a left hand limit at x = 4 which is equal to 9; and a right hand limit which is equal to 1. Since the two numbers do not coincide, the limit does not exist . 003 10.0 points Determine lim x x 1 x 2 ( x + 5) . 1. limit = 1 2. limit = 1 5 3. none of the other answers 4. limit = 0 5. limit = Version 100 EXAM 1 Radin (58280) 2 6. limit = correct Explanation: Now lim x x 1 = 1 . On the other hand, x 2 ( x + 5) > 0 for all small x , both positive and negative, while lim x x 2 ( x + 5) = 0 . Consequently, limit = . keywords: evaluate limit, rational function 004 10.0 points Let F be the function defined by F ( x ) = x 2 49  x 7  . Determine if lim x 7 F ( x ) exists, and if it does, find its value. 1. limit does not exist 2. limit = 14 correct 3. limit = 7 4. limit = 7 5. limit = 14 Explanation: After factorization, x 2 49  x 7  = ( x + 7)( x 7)  x 7  . But, for x < 7,  x 7  = ( x 7) . Thus F ( x ) = ( x + 7) , x < 7 , By properties of limits, therefore, the limit exists and lim x 7 F ( x ) = 14 . 005 10.0 points Determine lim x 8 x + 1 3 x 8 . 1. limit = 1 3 2. limit = 6 3. limit = 1 6 correct 4. limit doesnt exist 5. limit = 3 Explanation: After rationalizing the numerator we see that x + 1 3 = ( x + 1) 9 x + 1 + 3 = x 8 x + 1 + 3 ....
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This note was uploaded on 04/27/2008 for the course GEO 416M taught by Professor Staff during the Spring '08 term at University of Texas at Austin.
 Spring '08
 Staff

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