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Chapter 11: Q. 5 (page 879)

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

Short Answer

Expert verified

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

Step by step solution

01

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鈯�鈩�such that r'(t)鈮�0 onI. The unit tangent function is defined to be Tt=r'(t)r'(t).

02

Step 2. Explanation.

Let t0be 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 pointt0 at whichr't0=0.

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