M408K Hm. 7 Solutions

M408K Hm. 7 Solutions - Mahon, Kevin Homework 7 Due: Oct 13...

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Unformatted text preview: Mahon, Kevin Homework 7 Due: Oct 13 2005, 3:00 am Inst: Edward Odell 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 derivative of f when f ( x ) = 3 x sin5 x + 3 5 cos 5 x. 1. f ( x ) = 15 x cos 5 x + 6sin5 x 2. f ( x ) =- 15 x cos 5 x 3. f ( x ) = 15 x cos 5 x correct 4. f ( x ) = 15 x cos 5 x- 6sin5 x 5. f ( x ) = 15 cos 5 x Explanation: Since d dx sin x = cos x, d dx cos x =- sin x, it follows that f ( x ) = 3sin5 x + 15 x cos 5 x- 3sin5 x. Consequently, f ( x ) = 15 x cos 5 x . keywords: Stewart5e, 002 (part 1 of 1) 10 points Find f ( x ) when f ( x ) = x + 1 x- 1 2 . 1. f ( x ) =- 6( x + 2) ( x- 1) 3 2. f ( x ) = 4( x- 1) ( x + 1) 3 3. f ( x ) =- 4( x + 1) ( x- 1) 3 correct 4. f ( x ) = 6( x- 2) ( x + 1) 3 5. f ( x ) =- 4( x + 2) ( x- 1) 3 6. f ( x ) = 6( x- 1) ( x + 1) 3 Explanation: By the Chain and Quotient Rules, f ( x ) = 2 x + 1 x- 1 ( x- 1)- ( x + 1) ( x + 1) 2 . Consequently, f ( x ) =- 4( x + 1) ( x- 1) 3 . keywords: Stewart5e, 003 (part 1 of 1) 10 points Determine f ( x ) when f ( x ) = 1 + 2 x 1- x 2 . 1. f ( x ) =- 2 + x (1- x 2 ) 3 / 2 2. f ( x ) =- 2- x (1- x 2 ) 1 / 2 3. f ( x ) = 2 + x (1- x 2 ) 3 / 2 correct 4. f ( x ) =- 2 + x (1- x 2 ) 1 / 2 5. f ( x ) = 2- x (1- x 2 ) 3 / 2 6. f ( x ) = 2 + x (1- x 2 ) 1 / 2 Mahon, Kevin Homework 7 Due: Oct 13 2005, 3:00 am Inst: Edward Odell 2 Explanation: By the Product and Chain Rules, f ( x ) = 2 (1- x 2 ) 1 / 2 + 2 x (1 + 2 x ) 2(1- x 2 ) 3 / 2 = 2(1- x 2 ) + x (1 + 2 x ) (1- x 2 ) 3 / 2 . Consequently, f ( x ) = 2 + x (1- x 2 ) 3 / 2 . (Note: the Quotient Rule could have been used, but its simpler to use the Product Rule.) keywords: Stewart5e, 004 (part 1 of 1) 10 points Determine f ( x ) when f ( x ) = 3cos 2 x- 2sin 2 x. 1. f ( x ) = 6cos x + 4sin x 2. f ( x ) =- 6sin x + 4cos x 3. f ( x ) =- 10sin x cos x correct 4. f ( x ) = 10sin x cos x 5. f ( x ) =- 6sin x- 4cos x 6. f ( x ) = 2sin x cos x 7. f ( x ) =- 2sin x cos x Explanation: Since d dx sin x = cos x, d dx cos x =- sin x, the Chain Rule ensures that f ( x ) =- 6cos x sin x- 4sin x cos x. Consequently, f ( x ) =- 10sin x cos x . keywords: Stewart5e, 005 (part 1 of 1) 10 points Find the value of f (1) when f ( x ) = ( x 2 + 3) 1 / 2 + 3 x . 1. f (1) =- 3 2. f (1) =- 4 3. f (1) =- 9 2 4. f (1) =- 7 2 5. f (1) =- 5 2 correct Explanation: Using the Chain Rule and the fact that d dx x r = r x r- 1 holds for all values of r , we see that f ( x ) = x ( x 2 + 3) 1 / 2- 3 x 2 . At x = 1, therefore, f (1) =- 5 2 ....
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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. 7 Solutions - Mahon, Kevin Homework 7 Due: Oct 13...

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