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Q. 21

Expert-verifiedFound in: Page 860

Book edition
1st

Author(s)
Peter Kohn, Laura Taalman

Pages
1155 pages

ISBN
9781429241861

In Exercises 19–21 sketch the graph of a vector-valued function $r\left(t\right)=\left(x\left(t\right),y\left(t\right)\right)$ with the specified properties. Be sure to indicate the direction of increasing values of* t*.

Domain

$t\in \mathrm{\mathbb{R}},r\left(2\right)=\left(1,1\right),r\left(0\right)=\left(-3,3\right),r\left(-2\right)=\left(-5,-5\right)\underset{t\to -\infty}{\mathrm{lim}}x\left(t\right)=\infty ,\phantom{\rule{0ex}{0ex}}\underset{\mathrm{t}\to -\infty}{\mathrm{lim}}\mathrm{y}\left(\mathrm{t}\right)=-\infty ,\mathrm{and}\underset{t\to \infty}{\mathrm{lim}}\mathrm{r}\left(\mathrm{t}\right)=\left(0,0\right).$

The graph of the given vector-valued function with the specified properties is

The given vector-valued function is $r\left(t\right)=\left(x\left(t\right),y\left(t\right)\right).$ The given specified properties are $t\in \mathrm{\mathbb{R}},r\left(2\right)=\left(1,1\right),r\left(0\right)=\left(-3,3\right),r\left(-2\right)=\left(-5,-5\right)\underset{t\to -\infty}{\mathrm{lim}}x\left(t\right)=\infty ,$

$\underset{\mathrm{t}\to -\infty}{\mathrm{lim}}\mathrm{y}\left(\mathrm{t}\right)=-\infty ,\mathrm{and}\underset{t\to \infty}{\mathrm{lim}}\mathrm{r}\left(\mathrm{t}\right)=\left(0,0\right).$

The graph of the given vector-valued function with the specified properties is

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