quiz_04B - r ( t ) = h , i whenever either cos( t ) = 0 or...

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Math 213 — Quiz 4 Name Solution 1. Determine whether the curve r ( t ) = h cos 3 ( t ) , sin 3 ( t ) i is smooth. We need to check whether r 0 ( t ) is ever undefined or ever 0 . Note that r 0 ( t ) = - 3 cos 2 ( t ) sin( t ) i +3 sin 2 ( t ) cos( t ) j . This is always well defined. However
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Unformatted text preview: r ( t ) = h , i whenever either cos( t ) = 0 or sin( t ) = 0. So r ( t ) = when t = 0 , / 2 , , 3 / 2 ,... which shows that the curve is not smooth....
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This note was uploaded on 05/09/2008 for the course MATH 2130 taught by Professor Dorais during the Spring '08 term at Cornell University (Engineering School).

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