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Q. 1

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Found in: Page 774

### Calculus

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.

See the step by step solution

## Step 1. Given Information.

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

## Step 2. Explanation.

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

## Step 3. Find the direction.

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.

## Step 4. The graph.

The graph is as follows.