Answered: For each s ∈ (−1, 1), find the velocity…

For each s ∈ (−1, 1), find the velocity vector t¯(s), normal vector ¯n(s), binormal vector ¯b(s), curvature κ(s) and torsion τ (s)

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter7: Integration

Section7.5: The Area Between Two Curves

Problem 21E

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Question

For each s ∈ (−1, 1), find the velocity vector t¯(s), normal vector ¯n(s),
binormal vector ¯b(s), curvature κ(s) and torsion τ (s)

Let a : (−1, 1) → R³ be the curve defined by
1
S
( 1 +)
a(s) =
(1 + s)³/², (1 — s)³/²,

Quantities that have magnitude and direction but not position. Some examples of vectors are velocity, displacement, acceleration, and force. They are sometimes called Euclidean or spatial vectors.

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Step 1: Analysis and Introduction

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Step 2: Find the derivatives of the curve.

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Step 3: Find the velocity and tangent vector

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Step 4: Find the normal and binormal vector.

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Step 5: Find the curvature

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Step 6: Find the torsion

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