Unformatted text preview: with the instructor. (b) Suppose h : R → R is a function. We can get another parameterization of C by considering the composition f ( s ) = r ( h ( s ) ) This is called a reparameterization . Find a choice of h so that i. f (0) = r (0) ii. The length of the segment of C between f (0) and f ( s ) is s . (This is called parameterizing by arc length.) Check your answer with the instructor. (c) Without calculating anything, what is  f ( s )  ? (d) Draw a sketch of C . 3. Consider the curve C given by the parameterization r : R → R 3 where r ( t ) = (sin t ,cos t ,sin 2 t ). (a) Show that C is in the intersection of the surfaces z = x 2 and x 2 + y 2 = 1. (b) Use (a) to help you sketch the curve C . 4. As in 2(b), consider a reparameterization f ( s ) = r ( h ( s ) ) of an arbitrary vectorvalued function r : R → R 3 . Use the chain rule to calculate  f ( s )  in terms of r and h ....
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This note was uploaded on 02/20/2011 for the course MATH 241 taught by Professor Kim during the Fall '08 term at University of Illinois, Urbana Champaign.
 Fall '08
 Kim
 Calculus

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