(a) Explanation Given information: F ( x ) = f ( x ) g ( x ) , where f and g have derivatives of all orders. Proof: Given F ( x ) = f ( x ) g ( x ) d d x F ( x ) = F ' ( x ) = f ' ( x ) g ( x ) + f ( x ) g ' ( x ) F ' ' ( x ) = d d x ( F ' ( x ) ) = d d x ( f ' ( x ) g ( x ) + f ( x (b) To determine To find: formulas for F ' ' ' and F ( 4 ) . (c) To determine To show: Guess a formula for F ( n ) .

Bundle: Biocalculus: Calculus, Probability, And Statistics For The Life Sciences + Webassign Printed Access Card For Stewart/day's Biocalculus: Calculus For Life Sciences, 1st Edition, Multi-term

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ISBN: 9781305779037

Author: James Stewart, Troy Day

Publisher: Cengage Learning

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Question

Chapter 3.4, Problem 62E

(a)

To determine

To show: F''=f''g+2f'g'+fg'' .

(b)

To determine

To find:formulas for F''' and F(4) .

(c)

To determine

To show:Guess a formula for F(n) .

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Chapter 3.4, Problem 61E

Chapter 3.4, Problem 63E

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Chapter 3 Solutions

Bundle: Biocalculus: Calculus, Probability, And Statistics For The Life Sciences + Webassign Printed Access Card For Stewart/day's Biocalculus: Calculus For Life Sciences, 1st Edition, Multi-term

Ch. 3.1 - Prob. 1E Ch. 3.1 - Prob. 2E Ch. 3.1 - Prob. 3E Ch. 3.1 - Prob. 4E Ch. 3.1 - Prob. 5E Ch. 3.1 - Prob. 6E Ch. 3.1 - Prob. 7E Ch. 3.1 - Prob. 8E Ch. 3.1 - Prob. 9E Ch. 3.1 - Prob. 10E

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F ' ' = f ' ' g + 2 f ' g ' + f g ' ' .

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To show: F''=f''g+2f'g'+fg'' .

To find:formulas for F''' and F(4) .

To show:Guess a formula for F(n) .

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Chapter 3 Solutions