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Unformatted text preview: merino (aem2588) HW 1 chen (55405) 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 Evaluate lim x 2 (3 x 2 + 3 x 6) . Correct answer: 12. Explanation: Since a polynomial is continuous, lim x 2 (3 x 2 + 3 x 6) = (3 x 2 + 3 x 6) vextendsingle vextendsingle vextendsingle x =2 = 12 . 002 10.0 points If a ball is thrown into the air with a velocity of 60 ft/sec, its height in feet after t seconds is given by y = 60 t 16 t 2 . Find the average velocity of the ball for the time period beginning at t = 1 and lasting 1 / 4 seconds. 1. average vel. = 24 ft/sec correct 2. average vel. = 23 ft/sec 3. average vel. = 25 ft/sec 4. average vel. = 22 ft/sec 5. average vel. = 26 ft/sec Explanation: If the height of the ball after t seconds is given by y = y ( t ) = 60 t 16 t 2 , then the average velocity of the ball over a time interval [1 , t + h ] is avg. vel. = y (1 + h ) y (1) h . Now y (1 + h ) = 60(1 + h ) 16(1 + h ) 2 = 60(1 + h ) 16(1 + 2 h + h 2 ) = 44 + 28 h 16 h 2 , while y (1) = 60 16 = 44 . Thus y (1 + h ) y (1) h = 28 h 16 h 2 h = 28 16 h . Consequently, when h = 1 / 4, therefore, average velocity = 24 ft/sec . 003 10.0 points Evaluate lim x 2 (4 x 2 + 3 x 2) . 1. limit = 18 2. limit = 20 correct 3. limit = 19 4. limit doesnt exist 5. limit = 22 Explanation: By properties of limits, the limit can be taken term by term in f ( x ) = 4 x 2 + 3 x 2 . Consequently, lim x 2 (4 x 2 + 3 x 2) = 20 . merino (aem2588) HW 1 chen (55405) 2 004 10.0 points Determine which of the following functions is even. 1. f ( x ) = x 3 7 x 2. f ( x ) = 9 x 2 correct 3. f ( x ) = 5 x 3 4. f ( x ) = 9 x 3 + 5 x 2 + 4 5. f ( x ) = x 5 5 x 3 Explanation: 005 10.0 points Find the composition f g of the functions f ( x ) = 2 x + 4 x 2 , g ( x ) = 3 x + 1 . 1. ( f g )( x ) = 6 x 2 + 14 x + 4 x 2 2. ( f g )( x ) = 6 x + 6 x 2 3. ( f g )( x ) = 2 x + 4 9 x 2 + 6 x + 1 4. ( f g )( x ) = 6 x + 6 9 x 2 + 6 x + 1 correct 5. ( f g )( x ) = 4 x 2 + 16 x + 16 x 2 Explanation: The composition f g of functions f, g is defined by ( f g )( x ) = f ( g ( x )) . When f ( x ) = 2 x + 4 x 2 , g ( x ) = 3 x + 1 , therefore, ( f g )( x ) = 2 g ( x ) + 4 g ( x ) 2 = 2(3 x + 1) + 4 (3 x + 1) 2 = 6 x + 6 9 x 2 + 6 x + 1 . 006 10.0 points A glass window is designed in the shape of a rectangle surmounted by a semicircle as shown in the figure below h 7 The width of the window is 7 feet, but the height h is to be determined....
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This note was uploaded on 02/23/2011 for the course MATH 408C taught by Professor Knopf during the Spring '10 term at University of Texas at Austin.
 Spring '10
 KNOPF
 Differential Calculus

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