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

Info iconThis preview shows pages 1–4. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

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 > 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 ) ....
View Full Document

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.

Page1 / 10

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

This preview shows document pages 1 - 4. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online