Calculus (3rd Edition)

Published by W. H. Freeman
ISBN 10: 1464125260
ISBN 13: 978-1-46412-526-3

Chapter 12 - Parametric Equations, Polar Coordinates, and Conic Sections - 12.1 Parametric Equations - Exercises - Page 603: 45


The plot of $c(t)=(x(t),y(t))$ is Figure (III).

Work Step by Step

The graph of $x(t)$ goes up as $t$ increases, while $y(t)$ goes up and reaches a maximum point and then goes down to 0. In Figure (I) both $x$ and $y$ increases. In Figure II, $x$ increases but then decreases to 0; and $y$ never reaches 0. In Figure (III), $y$ increases and reaches the maximum height and then decreases to 0, while $x$ increases and reaches a certain value when $y$ reaches 0. So, the plot of $c(t)=(x(t),y(t))$ is Figure (III).
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