# HW 13 - Tran, Tony Homework 13 Due: Nov 20 2007, 3:00 am...

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Unformatted text preview: Tran, Tony Homework 13 Due: Nov 20 2007, 3:00 am Inst: Samuels 1 This print-out should have 21 questions. Multiple-choice 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 solution of the exponential equa- tion 4 7 x = 16 2 x- 16 . 1. x = 32 3 2. none of these 3. x =- 8 4. x =- 32 3 correct 5. x = 8 Explanation: By properties of exponents, 16 2 x- 16 = 4 4 x- 32 . Thus the equation can be rewritten as 4 7 x = 4 4 x- 32 , which after taking logs to the base 4 of both sides becomes 7 x = 4 x- 32 . Rearranging and solving we thus find that x =- 32 3 . keywords: 002 (part 1 of 1) 10 points Which of the following is the graph of f ( x ) = 2- 2- x- 1 ? 1. 2 4- 2- 4 2 4- 2- 4 2. 2 4- 2- 4 2 4- 2- 4 3. 2 4- 2- 4 2 4- 2- 4 4. 2 4- 2- 4 2 4- 2- 4 Tran, Tony Homework 13 Due: Nov 20 2007, 3:00 am Inst: Samuels 2 5. 2 4- 2- 4 2 4- 2- 4 correct 6. 2 4- 2- 4 2 4- 2- 4 Explanation: Since lim x 2- x = 0 , we see that lim x f ( x ) = 2 , in particular, f has a horizontal asymptote y = 2. This eliminates all but two of the graphs. On the other hand, f (0) = 3 2 , so the y-intercept of the given graph must occur at y = 3 2 . Consequently, the graph is of f is 2 4- 2- 4 2 4- 2- 4 keywords: 003 (part 1 of 1) 10 points Find the value of lim x 4 e 2 x- e- 2 x 2 e 2 x + 5 e- 2 x . 1. limit =- 1 2 2. limit = 3 7 3. limit =- 3 7 4. limit = 2 correct 5. limit = 1 2 6. limit =- 2 Explanation: After division we see that 4 e 2 x- e- 2 x 2 e 2 x + 5 e- 2 x = 4- e- 4 x 2 + 5 e- 4 x . On the other hand, lim x e- ax = 0 for all a &gt; 0. But then by properties of limits, lim x 4- e- 4 x 2 + 5 e- 4 x = 2 . Consequently, limit = 2 . keywords: exponential function, limit as in- finity 004 (part 1 of 1) 10 points Find the value of f (- 2) when f ( x ) = x 4 + e- 2 x . Tran, Tony Homework 13 Due: Nov 20 2007, 3:00 am Inst: Samuels 3 1. f (- 2) =- 32 + e 4 2. f (- 2) =- 32- 2 e 4 correct 3. f (- 2) = 64 + e 4 4. f (- 2) = 64- 2 e 4 5. f (- 2) =- 32- 2 e 6 Explanation: By the Chain rule, df dx = 4 x 3- 2 e- 2 x Consequently, f (- 2) =- 32- 2 e 4 . keywords: 005 (part 1 of 1) 10 points Determine the derivative of f ( x ) = e 3 x (cos 5 x + 4 sin 5 x ) . 1. f ( x ) = e 3 x (20 cos 5 x- 12 sin 5 x ) 2. f ( x ) = 3 e 3 x (20 cos 5 x- 5 sin 5 x ) 3. f ( x ) = 3 e 3 x (5 cos 5 x + 20 sin 5 x ) 4. f ( x ) = e 3 x (23 cos 5 x- 7 sin 5 x ) 5. f ( x ) = e 3 x (23 cos 5 x + 7 sin 5 x ) cor- rect 6. f ( x ) = e 3 x (7 cos 5 x + 23 sin 5 x ) Explanation: By the Product and Chain rules, f ( x ) = 3 e 3 x (cos 5 x + 4 sin 5 x ) + e 3 x (20 cos 5 x- 5 sin 5 x ) ....
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## This note was uploaded on 04/27/2008 for the course M 408k taught by Professor Schultz during the Fall '08 term at University of Texas at Austin.

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HW 13 - Tran, Tony Homework 13 Due: Nov 20 2007, 3:00 am...

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