Homework Help is Here – Start Your Trial Now!
Science
Advanced Physics
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

icon
Related questions
Question
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
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
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 5 steps

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer