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: 10

Answer

Cartesian equation: $x = y^{\frac 2 3}$
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Work Step by Step

(a) 1. Plot points determined by values for $t$. I used -3, -2, -1, 0, 1, 2 and 3. 2. Join them to produce a curve. 3. Draw the arrows indicating which direction the curve goes from $t = -3$ to $t= 3$ ----- (b) Solve for $t$ in the second equation: $y = t^3$ $\sqrt[3] y = t$ Substitute this value into the first equation: $x = t^2$ $x = (\sqrt [3] y)^2 = y^{\frac{2}{3}}$
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