Multivariable Calculus, 7th Edition

Published by Brooks Cole
ISBN 10: 0-53849-787-4
ISBN 13: 978-0-53849-787-9

Chapter 10 - Parametric Equations and Polar Coordinates - 10.1 Exercises - Page 665: 9

Answer

a) As t increases, x increases and y decreases. b) $y=1-x^{2}$ $x \geq 0$
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Work Step by Step

a) $x=\sqrt t$ $y=1-t$ When, t=-2 x=undefined y=3 t=-1 x=undefined y=2 t=0 x=0 y=1 t=1 x= 1 y=0 t=2 $x=\sqrt 2$ y=-1 t=3 $x=\sqrt 3$ y=-2 b) $x=\sqrt t$ $x^{2}=t$ $y=1-t$ $y=1-x^{2}$ From part a), we can infer that $x \geq 0$ because x is undefined at any negative t values.
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