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Chapter 11: Q. 8 (page 900)

Giveprecisemathematicaldefinitionsordescriptionsofeachoftheconceptsthatfollow.Thenillustratethedefinitionwithagraphoranalgebraicexample.theunittangentfunctionforadifferentiablevectorfunctionr(t)

Short Answer

Expert verified

T(t)=r'(t)r'(t)

Step by step solution

01

Step 1. Given information is:

A vector function r(t)

02

Step 2. Unit Tangent Function

Letr(t)beadifferentiablevectorfunctiononsomeintervalI鈯�Rsuchthatr'(t)鈮�0onI.Theunittangentfunctionisdefinedtobe:T(t)=r'(t)r'(t)

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