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To illustrate that the length of a smooth space curve does not depend on the parameterization used to compute it, calculate the length of one turn of the helix with the following parameterizations. a. r(t) = (cos 4t)i + (sin 4t)j + 4tk, 0sts5 b. r(t) = cos i+ sin Osts 47 c. r(t) = (cos t)i – (sin t)j – tk, - 2nsts0 Note that the helix shown to the right is just one example of such a helix, and does not exactly correspond to the parametrizations in parts a, b, or c.

To illustrate that the length of a smooth space curve does not depend on the parameterization used to compute it, calculate the length of one turn of the helix with the following parameterizations. a. r(t) = (cos 4t)i + (sin 4t)j + 4tk, 0sts5 b. r(t) = cos i+ sin Osts 47 c. r(t) = (cos t)i – (sin t)j – tk, - 2nsts0 Note that the helix shown to the right is just one example of such a helix, and does not exactly correspond to the parametrizations in parts a, b, or c.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter11: Topics From Analytic Geometry
Section: Chapter Questions
Problem 18T
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To illustrate that the length of a smooth space curve does not depend on the parameterization used to compute it, calculate the length of one turn of the helix with the following parameterizations. a. r(t) = (cos 4t)i + (sin 4t)j + 4tk, 0sts b. r(t) = cos i+ sin 0sts 4n c. r(t) = (cos t)i - (sin t)j – tk, - 2nsts0 Note that the helix shown to the right is just one example of such a helix, and does not exactly correspond to the parametrizations in parts a, b, or c. a. L (Type an exact answer, using n as needed.)
Transcribed Image Text:To illustrate that the length of a smooth space curve does not depend on the parameterization used to compute it, calculate the length of one turn of the helix with the following parameterizations. a. r(t) = (cos 4t)i + (sin 4t)j + 4tk, 0sts b. r(t) = cos i+ sin 0sts 4n c. r(t) = (cos t)i - (sin t)j – tk, - 2nsts0 Note that the helix shown to the right is just one example of such a helix, and does not exactly correspond to the parametrizations in parts a, b, or c. a. L (Type an exact answer, using n as needed.)
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