Let C be the curve r(t) = (2t, t², ť /3). (a) Compute the Frenet frame for C. (b) Calculate the values of T(t), N(t), and B(t) as t → ±00. (c) Compute the curvature of C.

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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3.
Let C be the curve r(t) = (2t, t², t/3).
(a) Compute the Frenet frame for C.
(b) Calculate the values of T(t), N(t), and B(t) ast → too.
(c) Compute the curvature of C.
(d) The torsion T(t) of a curve with position vector r(t) is given by
(r'(t) × r"(t)) - r"(t)
T(t) =
||r(t) × r"(t)||?
Compute the torsion of the curve C.
Transcribed Image Text:3. Let C be the curve r(t) = (2t, t², t/3). (a) Compute the Frenet frame for C. (b) Calculate the values of T(t), N(t), and B(t) ast → too. (c) Compute the curvature of C. (d) The torsion T(t) of a curve with position vector r(t) is given by (r'(t) × r"(t)) - r"(t) T(t) = ||r(t) × r"(t)||? Compute the torsion of the curve C.
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