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: 4


$(5.39,2.14), (1.72,1.37), (1,1), (1.37,1.72),$ and $(2.14,5.39)$ are consecutive points on the curve. The arrow points from $(5.39,2.14)$ to $(2.14,5.39)$.

Work Step by Step

Since $-2 \leq t \leq 2,$ plot the points where $t=-2,$ $t=-1,$ $t=0,$ $t=1,$ and $t=2$. You can find the $x$ and $y$ coordinates of each point by plugging the value of $t$ into the given formulas for $x$ and $y$. A calculator will be necessary. For instance, when $t=-2,$ $$x = e^{-(-2)} + (-2) \approx 5.39$$$$y = e^{(-2)} - (-2) \approx 2.14$$ Therefore, $t=-2$ corresponds to the point $(5.39,2.14)$. The same calculation gives: $(1.72,1.37)$ for $t=-1$ $(1,1)$ for $t=0$ $(1.37,1.72)$ for $t=1$ $(2.14,5.39)$ for $t=2$ Plot these five points and connect them with a curve (in order of increasing $t$), as shown. As $t$ increases from $-2$ to $2$, the curve is traced from $(5.39,2.14)$ to $(2.14,5.39)$, so an arrow should be drawn on the curve in that direction, as shown.
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