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: 2


$(9,-15), (4,0), (1,3), (0,0), (1,-3), (4,0)$ (repeated), and $(9,15)$ are consecutive points on the curve. The arrow points from $(9,-15)$ to $(9,15)$.

Work Step by Step

Since $-3 \leq t \leq 3,$ plot the points where $t=-3,$ $t=-2,$ $t=-1,$ $t=0,$ $t=1,$ $t=2,$ and $t=3$. You can find the $x$ and $y$ coordinates of each point by plugging the value of $t$ into the given formulas for $x$ and $y$. For instance, when $t=-3,$ $$x = (-3)^2 = 9$$$$y = (-3)^3 - 4(-3) = -15$$ Therefore, $t=-3$ corresponds to the point $(9,-15)$. The same calculation gives: $(4,0)$ for $t=-2$ $(1,3)$ for $t=-1$ $(0,0)$ for $t=0$ $(1,-3)$ for $t=1$ $(4,0)$ for $t=2$ $(9,15)$ for $t=3$ Plot these seven points and connect them with a curve (in order of increasing $t$), as shown. As $t$ increases from $-3$ to $3$, the curve is traced from $(9,-15)$ to $(9,15)$, so an arrow should be drawn on the curve in that direction, as shown.
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