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Unformatted text preview: Version 100 K Final Exam gualdani (56410) 1 This printout should have 25 questions. Multiplechoice questions may continue on the next column or page find all choices before answering. 001 10.0 points Find the derivative of f when f ( x ) = 6 x 2 + 2 x 3 + 3 . 1. f ( x ) = 6 parenleftBig 1 2 x 5 x 4 parenrightBig 2. f ( x ) = 3 parenleftBig 1 2 x 5 x 4 parenrightBig 3. f ( x ) = 6 parenleftBig 2 x 5 + 1 x 4 parenrightBig 4. f ( x ) = 3 parenleftBig 2 x 4 1 x 3 parenrightBig 5. none of the other answers 6. f ( x ) = 3 parenleftBig 2 x 4 + 1 x 3 parenrightBig 7. f ( x ) = 6 parenleftBig 2 x 5 1 x 4 parenrightBig correct Explanation: Since d dx ( x r ) = rx r 1 holds for all r , we see that f ( x ) = 12 x 6 x 4 . Consequently, f ( x ) = 6 parenleftBig 2 x 5 1 x 4 parenrightBig . keywords: derivatives, negative powers 002 10.0 points Find the derivative of f when f ( x ) = (2 3 x ) e 2 x +9 . 1. f ( x ) = (7 + 6 x ) e 2 x +9 2. f ( x ) = (7 6 x ) e 2 x +9 3. f ( x ) = (4 6 x ) e 2 x +9 4. f ( x ) = (1 6 x ) e 2 x +9 correct 5. f ( x ) = (1 + 6 x ) e 2 x +9 Explanation: By the Product and Chain Rules, f ( x ) = 3 e 2 x +9 + 2(2 3 x ) e 2 x +9 . Consequently, f ( x ) = (1 6 x ) e 2 x +9 . 003 10.0 points Find the derivative of f when f ( ) = ln(sin 5 ) . 1. f ( ) = 5 tan5 2. f ( ) = 5 cot5 correct 3. f ( ) = tan 5 4. f ( ) = 5 sin 5 5. f ( ) = cot5 6. f ( ) = 1 cos 5 Explanation: Version 100 K Final Exam gualdani (56410) 2 By the Chain Rule, f ( ) = 1 sin(5 ) d d (sin 5 ) = 5 cos5 sin 5 . Consequently, f ( ) = 5 cot5 . 004 10.0 points Find f ( x ) when f ( x ) = x 2 ln ( 5 + x 2 ) . 1. f ( x ) = 2 x 8 x 3 (5 + x 2 ) 2 2. f ( x ) = 2 x + 4 x 3 5 + x 2 3. f ( x ) = 8 x x 3 5 + x 2 4. f ( x ) = 8 x + 2 x 3 (8 + x 2 ) 2 5. f ( x ) = 8 x + 2 x 3 5 + x 2 correct Explanation: By the Chain Rule, f ( x ) = 2 x 2 x 5 + x 2 . Consequently, after simplification, f ( x ) = 8 x + 2 x 3 5 + x 2 . 005 10.0 points Determine the derivative of f ( x ) = 5 sin 1 ( x/ 3) . 1. f ( x ) = 3 9 x 2 2. f ( x ) = 5 1 x 2 3. f ( x ) = 3 1 x 2 4. f ( x ) = 15 1 x 2 5. f ( x ) = 5 9 x 2 correct 6. f ( x ) = 15 9 x 2 Explanation: Use of d dx sin 1 ( x ) = 1 1 x 2 , together with the Chain Rule shows that f ( x ) = 5 radicalbig 1 ( x/ 3) 2 parenleftBig 1 3 parenrightBig . Consequently, f ( x ) = 5 9 x 2 ....
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This note was uploaded on 10/08/2010 for the course MATH 408K taught by Professor Gualdani during the Fall '09 term at University of Texas at Austin.
 Fall '09
 Gualdani

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