hw14 - Granillo Yvette – Homework 14 – Due Dec 1 2005...

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Unformatted text preview: Granillo, Yvette – Homework 14 – Due: Dec 1 2005, 3:00 am – Inst: Edward Odell 1 This print-out should have 17 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 Differentiate the function f ( x ) = cos(ln2 x ) . 1. f ( x ) = sin(ln2 x ) x 2. f ( x ) =- sin(ln2 x ) x correct 3. f ( x ) = 1 cos(ln2 x ) 4. f ( x ) =- 2sin(ln2 x ) x 5. f ( x ) = 2sin(ln2 x ) x 6. f ( x ) =- sin(ln2 x ) Explanation: By the Chain Rule f ( x ) =- sin(ln2 x ) x . keywords: Stewart5e, 002 (part 1 of 1) 10 points Differentiate the function f ( t ) = 2 + ln t 1- ln t . 1. f ( t ) =- 1ln t t (2 + ln t ) 2 2. f ( t ) =- 3 (1- ln t ) 2 3. f ( t ) =- 3 t (1- ln t ) 2 4. f ( t ) = 3 t (1- ln t ) 2 correct 5. f ( t ) = 1 t (2 + ln t ) 2 6. f ( t ) = 1ln t (2 + ln t ) 2 Explanation: By the Quotient Rule, f ( t ) = (1- ln t )(1 /t ) + (2 + ln t )(1 /t ) (1- ln t ) 2 = (1- ln t ) + (2 + ln t ) t (1- ln t ) 2 . Consequently, f ( t ) = 3 t (1- ln t ) 2 . keywords: Stewart5e, 003 (part 1 of 1) 10 points Find the derivative of f when f ( x ) = 2ln s 2 x 2- 1 2 x 2 + 1 . 1. f ( x ) = 8 x 4 x 4- 1 correct 2. f ( x ) =- 8 x 2 x 4- 1 3. f ( x ) =- 4 x 2 x 2- 1 4. f ( x ) = 4 x 2 x 2- 1 5. f ( x ) =- 4 x 4 x 2- 1 6. f ( x ) = 8 x 2 x 4- 1 Granillo, Yvette – Homework 14 – Due: Dec 1 2005, 3:00 am – Inst: Edward Odell 2 7. f ( x ) =- 8 x 4 x 4- 1 8. f ( x ) = 4 x 4 x 2- 1 Explanation: Properties of logs ensure that 2ln s 2 x 2- 1 2 x 2 + 1 = ln(2 x 2- 1)- ln(2 x 2 + 1) . By the Chain rule, therefore, f ( x ) = 4 x 2 x 2- 1- 4 x 2 x 2 + 1 . Consequently, f ( x ) = 8 x 4 x 4- 1 . keywords: Stewart5e, 004 (part 1 of 1) 10 points Find the derivative of f when f ( x ) = 4 · 5 x- 4 x 5 ln5 . 1. f ( x ) = ln 5(4 · 5 x- 4 x 4 ) 2. f ( x ) = ln 5(4 · 5 x- 20 x 4 ) correct 3. f ( x ) = ln 5(4 · 5 x- 20 x 5 ) 4. f ( x ) = ln 5(4 · 5 x- 1- 20 x 4 ) 5. f ( x ) = log 4 5(4 · 5 x- 20 x 4 ) Explanation: Note that 5 x = e x ln 5 ....
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hw14 - Granillo Yvette – Homework 14 – Due Dec 1 2005...

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