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Q. 1

Expert-verifiedFound in: Page 774

Book edition
1st

Author(s)
Peter Kohn, Laura Taalman

Pages
1155 pages

ISBN
9781429241861

Sketching parametric equations: Sketch the curves defined by the given sets of parametric equations. Indicate the direction of motion on each curve.

1. $x={t}^{2}$, $y={t}^{3}$, $t\in \left[-2,2\right]$.

The required graph is as follows,

The direction of the curve is upward.

The equations are $x={t}^{2}$ and $y={t}^{3}$ such that $t\in \left[-2,2\right]$.

Using equations, make a table that contains the coordinates of several points on the curve.

t | -2 | -1 | 0 | 1 | 2 |

$x={t}^{2}$ | 4 | 1 | 0 | 1 | 4 |

$y={t}^{3}$ | -8 | -1 | 0 | 1 | 8 |

Find derivatives of the parametric equations to check the direction of motion along the parametric curve with increasing values of t.

$\frac{dx}{dt}=2t$

$\frac{dy}{dt}=3{t}^{2}$

For all values of *t* , $\frac{dx}{dt}>0$ so curve is increasing.

The graph is as follows.

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