Consider the following vector function. r(t) = (6t², sin(t) - t cos(t), cos(t) + t sin(t)), t> 0 (a) Find the unit tangent and unit normal vectors T(t) and N(t). T(t) = N(t) = (b) Use this formula to find the curvature. x(t) = Consider the following vector function.

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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Consider the following vector function.
r(t) = (6t², sin(t) - t cos(t), cos(t) + t sin(t)), t> 0
(a) Find the unit tangent and unit normal vectors T(t) and N(t).
T(t) =
N(t)
(b) Use this formula to find the curvature.
k(t)
Consider the following vector function.
r(t) = ( 4t₁ -
t₁ =2²/₁2², 1²)
(a) Find the unit tangent and unit normal vectors T(t) and N(t).
T(t) =
N(t)
=
(b) Use the formula x(t)
k(t) =
=
IT'(t)|
Ir'(t)|
to find the curvature.
Transcribed Image Text:Consider the following vector function. r(t) = (6t², sin(t) - t cos(t), cos(t) + t sin(t)), t> 0 (a) Find the unit tangent and unit normal vectors T(t) and N(t). T(t) = N(t) (b) Use this formula to find the curvature. k(t) Consider the following vector function. r(t) = ( 4t₁ - t₁ =2²/₁2², 1²) (a) Find the unit tangent and unit normal vectors T(t) and N(t). T(t) = N(t) = (b) Use the formula x(t) k(t) = = IT'(t)| Ir'(t)| to find the curvature.
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