HW13 - Jolley, Garrett – Homework 13 – Due: Nov 20...

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Unformatted text preview: Jolley, Garrett – Homework 13 – Due: Nov 20 2007, 3:00 am – Inst: R Heitmann 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 2 3 x = 4 x +12 . 1. x =- 24 2. x = 12 3. x =- 12 4. x = 24 correct 5. none of these Explanation: By properties of exponents, 4 x +12 = 2 2 x +24 . Thus the equation can be rewritten as 2 3 x = 2 2 x +24 , which after taking logs to the base 2 of both sides becomes 3 x = 2 x + 24 . Rearranging and solving we thus find that x = 24 . keywords: 002 (part 1 of 1) 10 points Which of the following is the graph of f ( x ) = 2- x- 1- 2 ? 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 Jolley, Garrett – Homework 13 – Due: Nov 20 2007, 3:00 am – Inst: R Heitmann 2 5. 2 4- 2- 4 2 4- 2- 4 6. 2 4- 2- 4 2 4- 2- 4 correct 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 →∞ µ 4 e 3 x + e- 3 x 2 e 3 x- 3 e- 3 x ¶ . 1. limit =- 3 5 2. limit =- 2 3. limit =- 1 2 4. limit = 3 5 5. limit = 2 correct 6. limit = 1 2 Explanation: After division we see that 4 e 3 x + e- 3 x 2 e 3 x- 3 e- 3 x = 4 + e- 6 x 2- 3 e- 6 x . On the other hand, lim x →∞ e- ax = 0 for all a > 0. But then by properties of limits, lim x →∞ 4 + e- 6 x 2- 3 e- 6 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 2 + 4 e- 4 x . Jolley, Garrett – Homework 13 – Due: Nov 20 2007, 3:00 am – Inst: R Heitmann 3 1. f (- 2) =- 4- 16 e 8 correct 2. f (- 2) =- 4 + 4 e 8 3. f (- 2) = 8 + 4 e 8 4. f (- 2) = 8- 16 e 8 5. f (- 2) =- 4- 16 e 10 Explanation: By the Chain rule, df dx = 2 x- 16 e- 4 x Consequently, f (- 2) =- 4- 16 e 8 . keywords: 005 (part 1 of 1) 10 points Determine the derivative of f ( x ) = e 2 x (cos 3 x + 5 sin 3 x ) . 1. f ( x ) = e 2 x (7 cos 3 x + 17 sin 3 x ) 2. f ( x ) = 2 e 2 x (3 cos 3 x + 15 sin 3 x ) 3. f ( x ) = e 2 x (15 cos 3 x- 10 sin 3 x ) 4. f ( x ) = e 2 x (17 cos 3 x + 7 sin 3 x ) cor- rect 5. f ( x ) = e 2 x (17 cos 3 x- 7 sin 3 x ) 6. f ( x ) = 2 e 2 x (15 cos 3 x- 3 sin 3 x ) Explanation: By the Product and Chain rules, f ( x ) = 2 e 2 x (cos 3 x + 5 sin 3 x ) + e 2 x (15 cos 3 x- 3 sin 3 x ) ....
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This note was uploaded on 10/29/2008 for the course M 408k taught by Professor Schultz during the Spring '08 term at University of Texas.

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HW13 - Jolley, Garrett – Homework 13 – Due: Nov 20...

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