Solutions HW 14 - mao (tm23477) Hw 14 gualdani (57180) 1...

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Unformatted text preview: mao (tm23477) Hw 14 gualdani (57180) 1 This print-out should have 18 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 ) = 5 sin 1 x + tan 1 x . 1. f (1) = 11 4 correct 2. f (1) = 9 4 3. f (1) = 7 4 4. f (1) = 5 4 5. f (1) = 3 4 Explanation: Since sin 1 (1) = 2 , tan 1 (1) = 4 , we see that f (1) = parenleftBig 5 2 + 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. 6 2. 5 3. 7 4. 4 5. 3 correct 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 4. y = x x 2 + 7 correct 5. y = x 2 + 7 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 mao (tm23477) Hw 14 gualdani (57180) 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 Simplify the expression f ( x ) = sin ( tan 1 x ) . 1. f ( x ) = radicalbig 1 + x 2 2. f ( x ) = 1 1- x 2 3. f ( x ) = radicalbig 1- x 2 4. f ( x ) = x 1 + x 2 correct 5. f ( x ) = x 1- x 2 6. f ( x ) = 1 1 + x 2 Explanation: By definition f ( x ) = sin where x = tan . But then by Pythagoras, sin = x 1 + x 2 . Consequently, f ( x ) = x 1 + x 2 . 005 10.0 points Determine if lim x sin 1 parenleftbigg 3 + 2 x 4 + 2 x parenrightbigg exists, and if it does, find its value. 1. limit does not exist 2. limit = 0 3. limit = 3 4. limit = 2 correct 5. limit = 6 6. limit = 4 Explanation: Since lim x 3 + 2 x 4 + 2 x = 1 , we see that lim x sin 1 parenleftbigg 3 + 2 x 4 + 2 x parenrightbigg exists, and that the...
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Solutions HW 14 - mao (tm23477) Hw 14 gualdani (57180) 1...

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