(a) Explanation Given: A parametric curve r ( t ) = 〈 t cos t , t sin t , t 〉 . Calculation: In order to show that the given parametric curve lies on the cone x 2 + y 2 = z 2 , we will plug r ( t ) = 〈 t cos t , t sin t , t 〉 in the cone x 2 + y 2 = z 2 ... (b) To determine To sketch: The given parametric curve r ( t ) = 〈 t cos t , t sin t , t 〉 and the cone x 2 + y 2 = z 2 .

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ISBN: 9781319050733

Author: Rogawski

Publisher: MAC HIGHER

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Question

Chapter 14.1, Problem 25E

(a)

To determine

To show:

That the given parametric curve lies on the cone $x^{2} + y^{2} = z^{2}$ .

(b)

To determine

To sketch:

The given parametric curve $r (t) = 〈 t \cos t, t \sin t, t 〉$ and the cone $x^{2} + y^{2} = z^{2}$ .

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Chapter 14.1, Problem 24E

Chapter 14.1, Problem 26E

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Chapter 14 Solutions

CALCULUS (CLOTH)

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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That the given parametric curve lies on the cone x 2 + y 2 = z 2 .

Solution Summary: The author illustrates how the parametric curve lies on the cone x 2 + y 2 = z 2.

Concept explainers

To show:

That the given parametric curve lies on the cone $x^{2} + y^{2} = z^{2}$ .

To sketch:

The given parametric curve $r (t) = 〈 t \cos t, t \sin t, t 〉$ and the cone $x^{2} + y^{2} = z^{2}$ .

Want to see the full answer?

Chapter 14 Solutions

That the given parametric curve lies on the cone x 2 + y 2 = z 2 .

Solution Summary: The author illustrates how the parametric curve lies on the cone x 2 + y 2 = z 2.

Concept explainers

To show: That the given parametric curve lies on the cone x2+y2=z2.

To sketch: The given parametric curve r(t)=〈tcost,tsint,t〉 and the cone x2+y2=z2.

Want to see the full answer?

Chapter 14 Solutions

To show:

That the given parametric curve lies on the cone $x^{2} + y^{2} = z^{2}$ .

To sketch:

The given parametric curve $r (t) = 〈 t \cos t, t \sin t, t 〉$ and the cone $x^{2} + y^{2} = z^{2}$ .