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Unformatted text preview: Jolley, Garrett Exam 3 Due: Dec 5 2007, 1:00 am Inst: R Heitmann 1 This printout should have 18 questions. Multiplechoice questions may continue on the next column or page find all choices before answering. The due time is Central time. 001 (part 1 of 1) 10 points Find the value of x when x = 8 log 3 1 9 + 9 log 4 16 . 1. x = 2 correct 2. x = 4 3. x = 4 4. x = 3 5. x = 2 6. x = 3 Explanation: By properties of logs, log 3 1 9 = log 3 1 (3) 2 = 2 , while log 4 16 = log 4 (4) 2 = 2 . Consequently, x = 18 16 = 2 . keywords: 002 (part 1 of 1) 10 points If $200 is invested at an annual interest rate of 8%, determine the value of the investment after 4 years when interest is compounded continuously, leaving your answer in expo nential form. 1. Amount = $2 e . 32 2. Amount = $200 e . 32 3. Amount = $200 e 32 4. Amount = $200 e . 32 correct 5. Amount = $2 e 32 Explanation: When $ P is invested at an annual interest rate of r % compounded continuously, then af ter n years the investment is worth $ Pe rn/ 100 . When P = 200, r = 8 and n = 4, therefore, Amount = $200 e . 32 . keywords: 003 (part 1 of 1) 10 points Simplify the expression y = sin tan 1 x 6 by writing it in algebraic form. 1. y = x x 2 + 6 correct 2. y = 6 x 2 + 6 3. y = x 2 + 6 6 4. y = x x 2 6 5. y = x x 2 + 6 Explanation: The given expression has the form y = sin where tan = x 6 , 2 < < 2 . To determine the value of sin given the value of tan , we can apply Pythagoras theorem to the right triangle Jolley, Garrett Exam 3 Due: Dec 5 2007, 1:00 am Inst: R Heitmann 2 6 x p x 2 + 6 From this it follows that y = sin = x x 2 + 6 . Alternatively, we can use the trig identity csc 2 = 1 + cot 2 to determine sin . keywords: 004 (part 1 of 1) 10 points Find the inverse function, f 1 , of f when f is defined by f ( x ) = 5 x 6 , x 6 5 . 1. f 1 ( x ) = 1 5 p x 2 6 , x 2. f 1 ( x ) = 1 5 ( x 2 + 6) , x 5 6 3. f 1 ( x ) = 1 6 p x 2 5 , x 4. f 1 ( x ) = 1 5 ( x 2 + 6) , x correct 5. f 1 ( x ) = 1 6 ( x 2 5) , x 6 5 6. f 1 ( x ) = 1 6 p x 2 + 5 , x 5 6 Explanation: Since f has domain [ 6 5 , ) and is increasing on its domain, the inverse of f exists and has range [ 6 5 , ); furthermore, since f has range [0 , ), the inverse of f has domain [0 , ). To determine f 1 we solve for x in y = 5 x 6 and then interchange x, y . Solving first for x , we see that 5 x = y 2 + 6 . Consequently, f 1 is defined on [0 , ) by f 1 ( x ) = 1 5 ( x 2 + 6) . keywords: 005 (part 1 of 1) 10 points When g is the inverse of f ( x ) = x 3 + 2 x 1 , find the value of g (11)....
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This note was uploaded on 10/29/2008 for the course M 408k taught by Professor Schultz during the Fall '08 term at University of Texas at Austin.
 Fall '08
 schultz

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