Explanation Given Info: Given r ( t ) = w + t v Formula Used: If r ( t ) represents parametric equation of any structure then its arc length is given by, s ( t ) = ∫ 0 t ‖ r ( u ) · ‖ d u Where, ‖ r ( t ) · ‖ = ( d x d t ) 2 + ( d y d t ) 2 + ( d z d t ) 2 Calculation: r ( t ) = w + t v Therefore, r · ( t ) = v and ‖ To determine b) To find an arc length parametrization of the line.

4th Edition

ISBN: 9781319323394

Author: Rogawski

Publisher: MAC HIGHER

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Chapter 14.3, Problem 29E

To determine

a)

To show that the arc length function of $r (t) = w + t v$ is equal to $s (t) = t ‖ v ‖$

To determine

b)

To find an arc length parametrization of the line.

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Chapter 14.3, Problem 28E

Chapter 14.3, Problem 30E

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Chapter 14 Solutions

CALCULUS W/SAPLING ACCESS >IC<

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) To show that the arc length function of r ( t ) = w + t v is equal to s ( t ) = t ‖ v ‖

Solution Summary: The author explains that the arc length function of r (t) = w + t v is equal to s

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a)

To show that the arc length function of $r (t) = w + t v$ is equal to $s (t) = t ‖ v ‖$

b)

To find an arc length parametrization of the line.

Want to see the full answer?

Chapter 14 Solutions

a) To show that the arc length function of r ( t ) = w + t v is equal to s ( t ) = t ‖ v ‖

Solution Summary: The author explains that the arc length function of r (t) = w + t v is equal to s

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a) To show that the arc length function of r(t)=w+tv is equal to s(t)=t‖v‖

b) To find an arc length parametrization of the line.

Want to see the full answer?

Chapter 14 Solutions

a)

To show that the arc length function of $r (t) = w + t v$ is equal to $s (t) = t ‖ v ‖$

b)

To find an arc length parametrization of the line.