calc15 - pokharel (yp624) HW15 Radin (56520) 1 This...

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Unformatted text preview: pokharel (yp624) HW15 Radin (56520) 1 This print-out should have 17 questions. Multiple-choice questions may continue on the next column or page find all choices before answering. 001 10.0 points Find the value of f (- 1) when f ( x ) = tan 1 x- 6 sin 1 x . 1. f (- 1) = 15 4 2. f (- 1) = 9 4 3. f (- 1) = 17 4 4. f (- 1) = 13 4 5. f (- 1) = 11 4 correct Explanation: Since tan 1 (- 1) =- 4 , sin 1 (- 1) =- 2 , we see that f (- 1) = parenleftBig 3- 1 4 parenrightBig = 11 4 . 002 10.0 points Find the exact value of sin 1 parenleftBig 3 2 parenrightBig in the interval parenleftBig , 2 parenrightBig . 1. 4 2. 7 3. 6 4. 3 correct 5. 5 Explanation: We have to find x so that sin x = 3 2 , < x < 2 . Known trig values thus ensure that x = 3 . 003 10.0 points Simplify the expression y = sin parenleftbigg tan 1 x 7 parenrightbigg by writing it in algebraic form. 1. y = x x 2 + 7 2. y = 7 x 2 + 7 3. y = x x 2 + 7 correct 4. y = x 2 + 7 7 5. y = x x 2- 7 Explanation: The given expression has the form y = sin where tan = x 7 ,- 2 < < 2 . To determine the value of sin given the value of tan , we can apply Pythagoras theorem to the right triangle 7 x radicalbig x 2 + 7 pokharel (yp624) HW15 Radin (56520) 2 From this it follows that y = sin = x x 2 + 7 . Alternatively, we can use the trig identity csc 2 = 1 + cot 2 to determine sin . 004 10.0 points Determine if lim x tan 1 parenleftBigg 3 + 3 x 5 + x parenrightBigg exists, and if it does, find its value. 1. limit = 6 2. limit = 3 correct 3. limit = 4 4. limit = 2 5. limit does not exist 6. limit = 0 Explanation: Since lim x 3 + 3 x 5 + x = 3 , we see that lim x tan 1 parenleftBigg 3 + 3 x 5 + x parenrightBigg exists, and that the limit = tan 1 3 = 3 . 005 10.0 points Determine the derivative of f ( x ) = 5 sin 1 ( x/ 4) . 1. f ( x ) = 20 16- x 2 2. f ( x ) = 5 1- x 2 3. f ( x ) = 5 16- x 2 correct 4. f ( x ) = 20 1- x 2 5. f ( x ) = 4 16- x 2 6. f ( x ) = 4 1- 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/ 4) 2 parenleftBig 1 4 parenrightBig . Consequently, f ( x ) = 5 16- x 2 . 006 10.0 points Find the derivative of f when f ( x ) = parenleftBig tan 1 (2 x ) parenrightBig 2 . 1. f ( x ) = 2 4 + x 2 tan 1 (2 x ) 2. f ( x ) = sec 2 (2 x )tan(2 x ) 3. f ( x ) = 2 1 + 4 x 2 tan 1 (2 x ) pokharel (yp624) HW15 Radin (56520) 3 4. f ( x ) = 4 4 + x 2 tan 1 (2 x ) 5. f ( x ) = 4 1 + 4 x 2 tan 1 (2 x ) correct 6. f ( x ) = 4 sec 2 (2 x )tan(2 x ) Explanation: Since d dx tan 1 x = 1 1 + x 2 , the Chain Rule gives...
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This note was uploaded on 06/05/2010 for the course PHYS 92515 taught by Professor Tsoi during the Spring '10 term at University of Texas at Austin.

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calc15 - pokharel (yp624) HW15 Radin (56520) 1 This...

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