Explanation Given info. x ( t ) = ∫ 0 t sin u 2 2 d u , y ( t ) = ∫ 0 t cos u 2 2 d u Formula used: Let r ( t ) and T ( t ) be a differentiable vector and unit tangent vector respectively. Then the principal normal vector is N ( t ) = T ' ( t ) Here, T ( t ) = r ' ( t ) | r ' ( t ) | Calculation: r ( t ) = 〈 x ( t ) , y ( t ) 〉 x ( t ) = ∫ 0 t sin u 2 2 d u , y ( t ) = ∫ 0 t cos u 2 2 d u d x ( t ) d t = x ' ( t ) = d d t ∫ 0 t sin u 2 2 d u = sin t 2 2 y ( t ) = ∫ 0 t cos u 2 2 d u d y ( t ) d t = d d t ∫ 0 t cos u 2

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ISBN: 9781319323394

Author: Rogawski

Publisher: MAC HIGHER

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Chapter 14.4, Problem 40E

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The normal vector to the cornu spiral at $t = \sqrt{π}$ .

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Chapter 14.4, Problem 39E

Chapter 14.4, Problem 41E

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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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The normal vector to the cornu spiral at t = π .

Solution Summary: The author calculates the normal vector to the cornu spiral at t =. Let r and T be a differentiable vector and unit tangent vector respectively.

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To calculate:

The normal vector to the cornu spiral at $t = \sqrt{π}$ .

Want to see the full answer?

Chapter 14 Solutions

The normal vector to the cornu spiral at t = π .

Solution Summary: The author calculates the normal vector to the cornu spiral at t =. Let r and T be a differentiable vector and unit tangent vector respectively.

Videos

To calculate: The normal vector to the cornu spiral at t=π.

Want to see the full answer?

Chapter 14 Solutions

To calculate:

The normal vector to the cornu spiral at $t = \sqrt{π}$ .