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Unformatted text preview: silva (jrs4378) hw15 gualdani (56455) 1 This printout should have 15 questions. Multiplechoice 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 ) = 3 tan 1 x 4 sin 1 x . 1. f ( 1) = 13 4 2. f ( 1) = 9 4 3. f ( 1) = 11 4 4. f ( 1) = 7 4 5. f ( 1) = 5 4 correct Explanation: Since tan 1 ( 1) = 4 , sin 1 ( 1) = 2 , we see that f ( 1) = parenleftBig 2 3 4 parenrightBig = 5 4 . 002 10.0 points Simplify the expression y = sin parenleftbigg tan 1 x 5 parenrightbigg by writing it in algebraic form. 1. y = x 2 + 5 5 2. y = x x 2 + 5 3. y = x x 2 5 4. y = 5 x 2 + 5 5. y = x x 2 + 5 correct Explanation: The given expression has the form y = sin where tan = x 5 , 2 < < 2 . To determine the value of sin given the value of tan , we can apply Pythagoras theorem to the right triangle 5 x radicalbig x 2 + 5 From this it follows that y = sin = x x 2 + 5 . Alternatively, we can use the trig identity csc 2 = 1 + cot 2 to determine sin . keywords: TrigFunc, TrigFuncExam, 003 10.0 points Determine if lim x tan 1 parenleftbigg 3 + 2 x 4 + 2 x parenrightbigg exists, and if it does, find its value. 1. limit = 2 2. limit = 3 silva (jrs4378) hw15 gualdani (56455) 2 3. limit = 6 4. limit = 0 5. limit does not exist 6. limit = 4 correct Explanation: Since lim x 3 + 2 x 4 + 2 x = 1 , we see that lim x tan 1 parenleftbigg 3 + 2 x 4 + 2 x parenrightbigg exists, and that the limit = tan 1 1 = 4 . 004 10.0 points Determine the derivative of f ( x ) = 4 sin 1 ( x/ 3) . 1. f ( x ) = 12 1 x 2 2. f ( x ) = 12 9 x 2 3. f ( x ) = 4 9 x 2 correct 4. f ( x ) = 4 1 x 2 5. f ( x ) = 3 9 x 2 6. f ( x ) = 3 1 x 2 Explanation: Use of d dx sin 1 ( x ) = 1 1 x 2 , together with the Chain Rule shows that f ( x ) = 4 radicalbig 1 ( x/ 3) 2 parenleftBig 1 3 parenrightBig . Consequently, f ( x ) = 4 9 x 2 . 005 10.0 points Find the derivative of f when f ( x ) = parenleftBig tan 1 parenleftBig x 3 parenrightBigparenrightBig 2 ....
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 Spring '10
 Gualdani

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