Calculus Notes 11.1

# Calculus Notes 11.1 - Calculus-Stewart Dr Berg Summer 09 11.1 Curves Defined by Parametric Equations Parametric Equations Some curves are most

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Calculus- Stewart Dr. Berg Summer ‘09 Page 1 11.1 11.1 Curves Defined by Parametric Equations Parametric Equations Some curves are most easily defined by giving the x and y coordinates as functions of a third parameter t . Definition A parametric curve (in R 2 ) is a curve with coordinates given by parametric equations x = f ( t ) and y = g ( t ) . Example A What curve is represented by x = 2cos t and y = 2sin t ? Notice that x 2 + y 2 = (2cos t ) 2 + (2sin t ) 2 = 4 defines a circle of radius 2 centered at the origin. Example B What curve is represented by x = t 2 + t and y = 2 t 1 ? If we plot some points and connect the dots, we get this curve: The arrows on the graph indicate the direction of motion of the point ( x ( t ), y ( t )) as t increases. To find the equation in x and y , we solve y = 2 t 1 for t and substitute into x = t 2 + t . Indeed t = 1 2 ( y + 1) and x = t 2 + t = 1 2 ( y + 1) [ ] 2 + 1 2 ( y + 1) = 1 4 y 2 + y + 3 4 .

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Calculus- Stewart Dr. Berg Summer ‘09
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## This note was uploaded on 06/06/2010 for the course M 408 taught by Professor Hodges during the Spring '08 term at University of Texas at Austin.

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Calculus Notes 11.1 - Calculus-Stewart Dr Berg Summer 09 11.1 Curves Defined by Parametric Equations Parametric Equations Some curves are most

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