final2 - Granillo, Yvette Final 1 Due: May 10 2006, 10:00...

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Unformatted text preview: Granillo, Yvette Final 1 Due: May 10 2006, 10:00 pm Inst: E Schultz 1 This print-out should have 25 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 ( t ) = ln t 3- ln t . 1. f ( t ) = 3 ln t (3- ln t ) 2 2. f ( t ) = t (3- ln t ) 2 3. f ( t ) = t (3- ln t ) 2 4. f ( t ) = 3 ln t 3- ln t 5. f ( t ) = 3 t (3- ln t ) 2 correct 6. f ( t ) = ln t 3- ln t Explanation: By the Quotient Rule, f ( t ) = (3- ln t )(1 /t ) + (ln t )(1 /t ) (3- ln t ) 2 . Consequently, f ( t ) = 3 t (3- ln t ) 2 . keywords: Stewart5e, derivative, Quotient Rule, log function, 002 (part 1 of 1) 10 points Find the derivative of f when f ( x ) = 7 x cos 3 x- 4 sin 3 x. 1. f ( x ) =- 12 cos 3 x + 21 x sin 3 x 2. f ( x ) = 12 cos 3 x- 5 x sin 3 x 3. f ( x ) =- 21 x sin 3 x- 5 cos 3 x correct 4. f ( x ) =- 21 x sin 3 x- 12 cos 3 x 5. f ( x ) = 21 x sin 3 x- 5 cos 3 x Explanation: Using formulas for the derivatives of sine and cosine together with the Product and Chain Rules, we see that f ( x ) = 7 cos 3 x- 21 x sin 3 x- 12 cos 3 x =- 21 x sin 3 x- 5 cos 3 x . keywords: Stewart5e, 003 (part 1 of 1) 10 points Determine f ( x ) when f ( x ) = cos( e- x ) . 1. f ( x ) = e- x sin( e- x ) correct 2. f ( x ) = e- x cos( e- x ) 3. f ( x ) =- e- x sin( e- x ) 4. f ( x ) =- cos( e- x )- e- x 5. f ( x ) =- sin( e- x ) 6. f ( x ) = cos( e- x ) + e- x Explanation: By the Chain Rule, f ( x ) = sin( e- x ) d dx e- x . Consequently, f ( x ) = e- x sin( e- x ) . Granillo, Yvette Final 1 Due: May 10 2006, 10:00 pm Inst: E Schultz 2 keywords: Stewart5e, 004 (part 1 of 1) 10 points Find the derivative of f when f ( x ) = ln s 1 + 2 x 2 1- 2 x 2 . 1. f ( x ) = 4 x 1- 4 x 4 correct 2. f ( x ) = 2 x 1- 2 x 4 3. f ( x ) = 4 x 1- 2 x 4 4. f ( x ) =- 2 x 1- 4 x 4 5. f ( x ) =- 4 x 1- 4 x 4 6. f ( x ) =- 4 x 1- 2 x 4 7. f ( x ) = 2 x 1- 4 x 4 8. f ( x ) =- 2 x 1- 2 x 4 Explanation: Properties of logs ensure that ln s 1 + 2 x 2 1- 2 x 2 = 1 2 n ln(1 + 2 x 2 )- ln(1- 2 x 2 ) o . By the Chain rule, therefore, f ( x ) = 1 2 n 4 x 1 + 2 x 2 + 4 x 1- 2 x 2 o . Consequently, f ( x ) = 4 x 1- 4 x 4 . keywords: Stewart5e, 005 (part 1 of 1) 10 points Find the derivative of f when f ( x ) = 4 tan- 1 ( e 3 x ) . 1. f ( x ) = 4 1 + e 3 x 2. f ( x ) = 3 e 3 x 1 + e 3 x 3. f ( x ) = 4 9 + e 6 x 4. f ( x ) = 3 e 3 x 9 + e 6 x 5. f ( x ) = 12 e 3 x 1 + e 6 x correct 6. f ( x ) = 12 e 3 x 9 + e 3 x Explanation: By the Chain Rule, f ( x ) = 3 4 e 3 x 1 + e 6 x since d dx tan- 1 x = 1 1 + x 2 , ( e 3 x ) 2 = e 6 x . Consequently, f ( x ) = 12 e 3 x 1 + e 6 x ....
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final2 - Granillo, Yvette Final 1 Due: May 10 2006, 10:00...

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