Final3 - Granillo Yvette – Final 1 – Due 10:00 pm – Inst E Schultz 1 This print-out should have 25 questions Multiple-choice questions may

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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 4 + ln t . 1. f ( t ) = 4 ln t 4 + ln t 2. f ( t ) = 4 t (4 + ln t ) 2 correct 3. f ( t ) = ln t 4 + ln t 4. f ( t ) = t (4 + ln t ) 2 5. f ( t ) = t (4 + ln t ) 2 6. f ( t ) = 4 ln t (4 + ln t ) 2 Explanation: By the Quotient Rule, f ( t ) = (4 + ln t )(1 /t )- (ln t )(1 /t ) (4 + ln t ) 2 . Consequently, f ( t ) = 4 t (4 + 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 ) = 3 x cos 2 x- 4 sin 2 x. 1. f ( x ) =- 8 cos 2 x + 6 x sin 2 x 2. f ( x ) =- 6 x sin 2 x- 8 cos 2 x 3. f ( x ) =- 6 x sin 2 x- 5 cos 2 x correct 4. f ( x ) = 8 cos 2 x- 5 x sin 2 x 5. f ( x ) = 6 x sin 2 x- 5 cos 2 x Explanation: Using formulas for the derivatives of sine and cosine together with the Product and Chain Rules, we see that f ( x ) = 3 cos 2 x- 6 x sin 2 x- 8 cos 2 x =- 6 x sin 2 x- 5 cos 2 x . keywords: Stewart5e, 003 (part 1 of 1) 10 points Determine f ( x ) when f ( x ) = cos( e- x ) . 1. f ( x ) =- sin( e- x ) 2. f ( x ) =- e- x sin( e- x ) 3. f ( x ) = e- x sin( e- x ) correct 4. f ( x ) = e- x cos( e- x ) 5. f ( x ) = cos( e- x ) + 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 ) = 1 2 ln s 2 + x 2 2- x 2 . 1. f ( x ) = x 2- x 4 2. f ( x ) = x 4- x 4 3. f ( x ) =- x 2- x 4 4. f ( x ) = 2 x 4- x 4 correct 5. f ( x ) = 2 x 2- x 4 6. f ( x ) =- 2 x 2- x 4 7. f ( x ) =- 2 x 4- x 4 8. f ( x ) =- x 4- x 4 Explanation: Properties of logs ensure that 1 2 ln s 2 + x 2 2- x 2 = 1 4 n ln(2 + x 2 )- ln(2- x 2 ) o . By the Chain rule, therefore, f ( x ) = 1 4 n 2 x 2 + x 2 + 2 x 2- x 2 o . Consequently, f ( x ) = 2 x 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 9 + e 6 x 2. f ( x ) = 3 e 3 x 9 + e 6 x 3. f ( x ) = 3 e 3 x 1 + e 3 x 4. f ( x ) = 12 e 3 x 9 + e 3 x 5. f ( x ) = 4 1 + e 3 x 6. f ( x ) = 12 e 3 x 1 + e 6 x correct 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 . keywords: Stewart5e, 006 (part 1 of 1) 10 points Determine dy/dx when 3 cos x sin y = 5 ....
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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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Final3 - Granillo Yvette – Final 1 – Due 10:00 pm – Inst E Schultz 1 This print-out should have 25 questions Multiple-choice questions may

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