Q. 1 Sketching parametric equations: ... [FREE SOLUTION]

91影视

Chapter 9: Q. 1 (page 774)

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

Short Answer

Expert verified

The required graph is as follows,

The direction of the curve is upward.

Step by step solution

Step 1. Given Information.

The equations are $x = t^{2}$ and $y = t^{3}$ such that $t 鈭� [- 2, 2]$ .

Step 2. Explanation.

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

t	-2	-1	1	2
$x = t^{2}$	4	1	1	4
$y = t^{3}$	-8	-1	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.

$\frac{d x}{d t} = 2 t$

$\frac{d y}{d t} = 3 t^{2}$

For all values of t , $\frac{d x}{d t} > 0$ so curve is increasing.

Step 4. The graph.

The graph is as follows.

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

91影视

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

Short Answer

Step by step solution

Step 1. Given Information.

Step 2. Explanation.

Step 3. Find the direction.

Step 4. The graph.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Discrete Mathematics

Logic and Functions

Pure Maths

Decision Maths

Statistics

Probability and Statistics

Study anywhere. Anytime. Across all devices.

91影视

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鈭�-2,2.

Short Answer

Step by step solution

Step 1. Given Information.

Step 2. Explanation.

Step 3. Find the direction.

Step 4. The graph.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Discrete Mathematics

Logic and Functions

Pure Maths

Decision Maths

Statistics

Probability and Statistics

Study anywhere. Anytime. Across all devices.

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