M408K Hm. 6 Solutions

M408K Hm. 6 Solutions - Mahon, Kevin – Homework 6 –...

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Unformatted text preview: Mahon, Kevin – Homework 6 – Due: Oct 6 2005, 3:00 am – Inst: Edward Odell 1 This print-out should have 20 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 derivative of f when f ( x ) = 5sec x + 4cos x. 1. f ( x ) = sin x ( 5sec 2 x + 4 ) 2. f ( x ) = cos x ( 5csc 2 x- 4 ) 3. f ( x ) = sin x ( 5sec 2 x- 4 ) correct 4. f ( x ) = cos x ( 5csc 2 x + 4 ) 5. f ( x ) = sin x ( 4- 5sec 2 x ) 6. f ( x ) = cos x ( 4- 5csc 2 x ) Explanation: Since d dx (sec x ) = sec x tan x = sin x sec 2 x while d dx (cos x ) =- sin x, we see that f ( x ) = sin x ( 5sec 2 x- 4 ) . keywords: Stewart5e, 002 (part 1 of 1) 10 points Find the derivative of f when f ( x ) = 2 x- 5sin x. 1. f ( x ) = 5- cos x 2. f ( x ) = 5- sin x 3. f ( x ) = 2- 5cos x correct 4. f ( x ) = 2 + 5cos x 5. f ( x ) = 2- 5sin x 6. f ( x ) = 2 + 5sin x Explanation: Since d dx sin x = cos x, we see that f ( x ) = 2- 5cos x . keywords: Stewart5e, 003 (part 1 of 1) 10 points Differentiate y = tan x- 6 sec x . 1. y = cos x + sin x 2. y = 6cos x + sin x 3. y = 6cos x- sin x 4. y = cos x- sin x 5. y = cos x + 6sin x correct Explanation: y = tan x- 6 sec x y = sec x sec 2 x- (tan x- 6) sec x tan x sec 2 x = sec x ( sec 2 x- tan 2 x + 6tan x ) sec 2 x = 1 + 6tan x sec x Mahon, Kevin – Homework 6 – Due: Oct 6 2005, 3:00 am – Inst: Edward Odell 2 Alternate solution: Simplify y first: y = sin x- 6cos x y = cos x + 6sin x keywords: Stewart5e, 004 (part 1 of 1) 10 points Find the derivative of f when f ( x ) = 1 + sin x cos x . 1. f ( x ) = 1 sin x- 1 2. f ( x ) = 1 1 + sin x 3. f ( x ) = 1 cos x- 1 4. f ( x ) =- 1 1 + cos x 5. f ( x ) =- 1 sin x + 1 6. f ( x ) = 1 1- sin x correct 7. f ( x ) = 1 1- cos x 8. f ( x ) = 1 cos x + 1 Explanation: By the quotient rule, f ( x ) = cos 2 x + sin x (1 + sin x ) cos 2 x = ( cos 2 x + sin 2 x ) + sin x cos 2 x . But sin 2 x + cos 2 x = 1, so f ( x ) = 1 + sin x 1- sin 2 x = 1 + sin x (1- sin x )(1 + sin x ) . Consequently, f ( x ) = 1 1- sin x . keywords: Stewart5e, 005 (part 1 of 1) 10 points Find the derivative of f when f ( x ) = 3tan x + 2cot x. 1. f ( x ) = 3- 5cos 2 x sin 2 x cos 2 x correct 2. f ( x ) = 3 + 5cos x sin x cos x 3. f ( x ) = 3 + 5cos 2 x sin 2 x cos 2 x 4. f ( x ) = 3 + 5sin 2 x sin 2 x cos 2 x 5. f ( x ) = 3- 5cos x sin x cos x 6. f ( x ) = 3- 5sin 2 x sin 2 x cos 2 x Explanation: After differentiation f ( x ) = 3sec 2 x- 2csc 2 x = 3 cos 2 x- 2 sin 2 x = 3sin 2 x- 2cos 2 x sin 2 x cos 2 x . Now 3sin 2 x- 2cos 2 x = 3 ( 1- cos 2 x )- 2cos 2 x = 3- 5cos 2 x. Mahon, Kevin – Homework 6 – Due: Oct 6 2005, 3:00 am – Inst: Edward Odell 3 Consequently, f ( x ) = 3- 5cos 2 x sin 2 x cos 2 x ....
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This homework help was uploaded on 04/15/2008 for the course M 408k taught by Professor Schultz during the Fall '08 term at University of Texas at Austin.

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M408K Hm. 6 Solutions - Mahon, Kevin – Homework 6 –...

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