hw7 - Granillo, Yvette Homework 7 Due: Oct 13 2005, 3:00 am...

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Unformatted text preview: Granillo, Yvette 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 ) = 2 x sin5 x + 2 5 cos 5 x. 1. f ( x ) = 10 x cos 5 x correct 2. f ( x ) = 10 x cos 5 x + 4sin5 x 3. f ( x ) = 10 x cos 5 x- 4sin5 x 4. f ( x ) = 10cos 5 x 5. f ( x ) =- 10 x cos 5 x Explanation: Since d dx sin x = cos x, d dx cos x =- sin x, it follows that f ( x ) = 2sin5 x + 10 x cos 5 x- 2sin5 x. Consequently, f ( x ) = 10 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 ) =- 4( x + 1) ( x- 1) 3 2. f ( x ) =- 4( x- 2) ( x + 1) 3 3. f ( x ) = 6( x- 2) ( x + 1) 3 4. f ( x ) = 4( x- 1) ( x + 1) 3 correct 5. f ( x ) =- 6( 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 + x 1- 2 x 2 . 1. f ( x ) =- 1- 2 x (1- 2 x 2 ) 1 / 2 2. f ( x ) =- 1 + 2 x (1- 2 x 2 ) 1 / 2 3. f ( x ) = 1 + 2 x (1- 2 x 2 ) 1 / 2 4. f ( x ) =- 1 + 2 x (1- 2 x 2 ) 3 / 2 5. f ( x ) = 1 + 2 x (1- 2 x 2 ) 3 / 2 correct 6. f ( x ) = 1- 2 x (1- 2 x 2 ) 3 / 2 Granillo, Yvette Homework 7 Due: Oct 13 2005, 3:00 am Inst: Edward Odell 2 Explanation: By the Product and Chain Rules, f ( x ) = 1 (1- 2 x 2 ) 1 / 2 + 4 x (1 + x ) 2(1- 2 x 2 ) 3 / 2 = (1- 2 x 2 ) + 2 x (1 + x ) (1- 2 x 2 ) 3 / 2 . Consequently, f ( x ) = 1 + 2 x (1- 2 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 ) = 2cos 2 x + 3sin 2 x. 1. f ( x ) =- 4sin x- 6cos x 2. f ( x ) = 2sin x cos x correct 3. f ( x ) =- 10sin x cos x 4. f ( x ) = 4cos x + 6sin x 5. f ( x ) =- 2sin x cos x 6. f ( x ) =- 4sin x + 6cos x 7. f ( x ) = 10sin x cos x Explanation: Since d dx sin x = cos x, d dx cos x =- sin x, the Chain Rule ensures that f ( x ) =- 4cos x sin x + 6sin x cos x. Consequently, f ( x ) = 2sin x cos x . keywords: Stewart5e, 005 (part 1 of 1) 10 points Find the value of f (1) when f ( x ) = ( x 2 + 8) 1 / 2 + 1 x . 1. f (1) =- 1 3 2. f (1) = 2 3 3. f (1) = 0 4. f (1) =- 2 3 correct 5. f (1) = 1 3 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 + 8) 1 / 2- 1 x 2 ....
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This test prep was uploaded on 04/16/2008 for the course M 408k taught by Professor Schultz during the Spring '08 term at University of Texas at Austin.

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hw7 - Granillo, Yvette Homework 7 Due: Oct 13 2005, 3:00 am...

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