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, 0
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, 0
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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,
1 = 27
b. r(t) = cos
i+ sin
2
이, 0sts 4T
%3D
+
c. (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.
(1, 0,0)
1 = 0](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F5c9159da-a431-4a35-8439-34e918757ee3%2F9d9f2b60-04ec-4f53-a732-bf76682ef52f%2F8bvkc9f_processed.png&w=3840&q=75)
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,
1 = 27
b. r(t) = cos
i+ sin
2
이, 0sts 4T
%3D
+
c. (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.
(1, 0,0)
1 = 0
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