Chapter 10, Problem 30RE

### Calculus (MindTap Course List)

11th Edition
Ron Larson + 1 other
ISBN: 9781337275347

Chapter
Section

### Calculus (MindTap Course List)

11th Edition
Ron Larson + 1 other
ISBN: 9781337275347
Textbook Problem

# Using Parametric Equations In Exercises 27-34, sketch the curve represented by the parametric equations (indicate the orientation of the curve), and write the corresponding rectangular equation by eliminating the parameter. x = e t − 1 ,   y = e 3 t

To determine

To calculate: The corresponding rectangular equation by eliminating the parameters and plot the graph of the rectangular equation when the parametric equations are x=et1, y=e3t.

Explanation

Given:

The parametric equations are x=etâˆ’1, y=e3t

Calculation:

Consider the parametric equations.

x=etâˆ’1

y=e3t

To graph the parametric firstly find some values of x and y for different values of t.

For t=âˆ’âˆž

x=eâˆ’âˆžâˆ’1=âˆ’1y=eâˆ’âˆž=0

For t=0

x=e0âˆ’1=0y=e3Ã—0=1

For t=0.13

x=e0.13âˆ’1=0.13y=e3Ã—0.13=1.5

For t=0.23

x=e0.23âˆ’1=0.25y=e3Ã—0

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