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. (t) = (cos 4t)i + (sin 4t)j + 4tk, 0sts j+k0sts 4x (t)=(cos t)i-(sin t)j-tk, -2xsts0 (1)= [cos (2)] + [sin (1) 1 + 2 + 0 ²1

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question
t=2m
(1,0,0)=0
2m
t=ㅠ
비비
y
Transcribed Image Text:t=2m (1,0,0)=0 2m t=ㅠ 비비 y
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.
X
(t) = (cos 4t)i + (sin 4t)j + 4tk, 0sts-
Osts
(t) =
-[cos ()] + [sin ( + 0
i+
) ³ 1/ K.
(t)=(cost)i-(sin t)j-tk, -2x st≤0
j+=k0sts 4x
Transcribed Image Text: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. X (t) = (cos 4t)i + (sin 4t)j + 4tk, 0sts- Osts (t) = -[cos ()] + [sin ( + 0 i+ ) ³ 1/ K. (t)=(cost)i-(sin t)j-tk, -2x st≤0 j+=k0sts 4x
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