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Q. 1

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Calculus
Found in: Page 774
Calculus

Calculus

Book edition 1st
Author(s) Peter Kohn, Laura Taalman
Pages 1155 pages
ISBN 9781429241861

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Short Answer

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

1. x=t2, y=t3, t-2,2.

The required graph is as follows,

The direction of the curve is upward.

See the step by step solution

Step by Step Solution

Step 1. Given Information.

The equations are x=t2 and y=t3 such that t-2,2.

Step 2. Explanation.

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

t-2-1012
x=t241014
y=t3-8-1018

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.

dxdt=2t

dydt=3t2

For all values of t , dxdt>0 so curve is increasing.

Step 4. The graph.

The graph is as follows.

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