Book edition 1st

Author(s) Peter Kohn, Laura Taalman

Pages 1155 pages

ISBN 9781429241861

Answers without the blur.

Just sign up for free and you're in.

Short Answer

Sketch the curves defined by the given sets of parametric equations. Indicate the direction of motion on each curve. $x = t^{2} y = t^{3}, t \in [- 2, 2]$

The Curve plot

See the step by step solution

Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1: Given information

The parametric curves, $x = t^{2} y = t^{3}, t \in [- 2, 2]$

Step 2: Calculation

The goal is to draw the parametric curve.

Assume $- 2, 0, 1, 2$ when drawing the graph for the parametric equations.

Find the values of $x, y$ by substituting different $t$ values in the parametric equations.

The point $(x, y)$ When $t = - 2$ is,

$(x, y) = (t^{2}, t^{3})$

$(x, y) = ((- 2)^{2}, (- 2)^{3})$ [since by substituting $t = - 2]$

$(x, y) = (4, - 8)$ simplify

The point $(x, y)$ When $t = - 1$ is,

$(x, y) = (t^{2}, t^{3}) (x, y) = ((- 1)^{2}, (- 1)^{3}) [since by substituting t = - 1] (x, y) = (1, - 1) simplify$

The point $(x, y)$ When $t = 0$ is,

$(x, y) = (t^{2}, t^{3})$

$(x, y) = ((0)^{2}, (0)^{3}) [$ since by substituting $t = 0]$

$(x, y) = (0, 0)$ simplify

The point $(x, y)$ When $t = 1$ is,

(x, y) = (t^{2}, t^{3}) (x, y) = (1^{2}, 1^{3}) [since by substituting t = 1] (x, y) = (1, 1) simplify

The point $(x, y)$ When $t = 2$ is,

(x, y) = (t^{2}, t^{3}) (x, y) = (2^{2}, 2^{3}) [since by substituting t = 2] (x, y) = (4, 8) simplify

Step 3: Calculation

The tabular representation of the points is as follows,

The graphical representation is shown below,

Therefore, the solution is the required graph.

Find Study Materials for

Create Study Materials

Select your language

Calculus

Answers without the blur.

Short Answer

Sketch the curves defined by the given sets of parametric equations. Indicate the direction of motion on each curve. $x = t^{2} y = t^{3}, t \in [- 2, 2]$

Step by Step Solution

Step 1: Given information

Step 2: Calculation

Step 3: Calculation

Most popular questions for Math Textbooks

Want to see more solutions like these?

Recommended explanations on Math Textbooks

Select your language

Calculus

Answers without the blur.

Short Answer

Sketch the curves defined by the given sets of parametric equations. Indicate the direction of motion on each curve. x=t2y=t3,t∈[-2,2]

Step by Step Solution

Step 1: Given information

Step 2: Calculation

Step 3: Calculation

Most popular questions for Math Textbooks

Want to see more solutions like these?

Recommended explanations on Math Textbooks

Decision Maths

Probability and Statistics

Statistics

Mechanics Maths

Geometry

Calculus

Pure Maths

Sketch the curves defined by the given sets of parametric equations. Indicate the direction of motion on each curve. $x = t^{2} y = t^{3}, t \in [- 2, 2]$