Explanation f ' ( x ) = tan θ f ' ' ( x ) = sec 2 θ [ d θ d x ] = ( 1 + tan 2 θ ) d θ d x To determine b) Use the are length integral to show that d s d x = 1 + f ' ( x ) 2 To determine c) Now given a proof of using equation

3rd Edition

ISBN: 9781464125263

Author: Jon Rogawski, Colin Adams

Publisher: W.H. Freeman & Co

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Chapter 14.4, Problem 71E

To determine

a)

Use the relation $f' (x) = \tan θ$ prove that $\frac{d θ}{d x} = \frac{f'' (x)}{(1 + f' {(x)}^{2})}$

To determine

b)

Use the are length integral to show that $\frac{d s}{d x} = \sqrt{1 + f' {(x)}^{2}}$

To determine

c)

Now given a proof of using equation

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Chapter 14.4, Problem 70E

Chapter 14.4, Problem 72E

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Chapter 14 Solutions

Calculus - Standalone book

Ch. 14.1 - Prob. 1PQ Ch. 14.1 - Prob. 2PQ Ch. 14.1 - Prob. 3PQ Ch. 14.1 - Prob. 4PQ Ch. 14.1 - Prob. 5PQ Ch. 14.1 - Prob. 6PQ Ch. 14.1 - Prob. 1E Ch. 14.1 - Prob. 2E Ch. 14.1 - Prob. 3E Ch. 14.1 - Prob. 4E

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a) Use the relation f ' ( x ) = tan θ prove that d θ d x = f ' ' ( x ) ( 1 + f ' ( x ) 2 )

Solution Summary: The author explains that the curve y = f (x) is parameterized by r ( x ) = 1 + tan, d

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a)

Use the relation $f' (x) = \tan θ$ prove that $\frac{d θ}{d x} = \frac{f'' (x)}{(1 + f' {(x)}^{2})}$

b)

Use the are length integral to show that $\frac{d s}{d x} = \sqrt{1 + f' {(x)}^{2}}$

c)

Now given a proof of using equation

Want to see the full answer?

Chapter 14 Solutions

a) Use the relation f ' ( x ) = tan θ prove that d θ d x = f ' ' ( x ) ( 1 + f ' ( x ) 2 )

Solution Summary: The author explains that the curve y = f (x) is parameterized by r ( x ) = 1 + tan, d

Concept explainers

Videos

a) Use the relation f'(x)=tanθ prove that dθdx=f''(x)(1+f'(x)2)

b) Use the are length integral to show that dsdx=1+f'(x)2

c) Now given a proof of using equation

Want to see the full answer?

Chapter 14 Solutions

a)

Use the relation $f' (x) = \tan θ$ prove that $\frac{d θ}{d x} = \frac{f'' (x)}{(1 + f' {(x)}^{2})}$

b)

Use the are length integral to show that $\frac{d s}{d x} = \sqrt{1 + f' {(x)}^{2}}$

c)

Now given a proof of using equation