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Q. 5

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Calculus
Found in: Page 879
Calculus

Calculus

Book edition 1st
Author(s) Peter Kohn, Laura Taalman
Pages 1155 pages
ISBN 9781429241861

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Short Answer

Under what conditions does a differentiable vector-valued function r(t) not have a unit tangent vector at a point in the domain of r(t)?

A differentiable vector-valued function r(t) does not have a unit tangent vector at any point t0 in the domain of r(t) at which r't0=0.

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Step by Step Solution

TABLE OF CONTENTS :
TABLE OF CONTENTS

Step 1. Given Information.

The definition of the unit tangent vector is to let r(t) be a differentiable vector function on some interval I⊆ℝ such that r'(t)≠0 on I. The unit tangent function is defined to be Tt=r'(t)r'(t).

Step 2. Explanation.

Let t0 be any point in the domain of r(t). So, by the definition of unit tangent vector, r(t) does not contain a unit tangent vector at any point t0 at which r't0=0.

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