Warning: foreach() argument must be of type array|object, bool given in /var/www/html/web/app/themes/studypress-core-theme/template-parts/header/mobile-offcanvas.php on line 20

Use the results of Exercise 3 to analyze the direction of motion for the parametric curves given by the equations in Exercises 5–8

x=t3-t,y=t3+t3t

Short Answer

Expert verified

The curve moves up and to the right.

Step by step solution

01

Step: 1 Given information

The equations of parametersx=t3-t,y=t3+t3t

02

Calculation

Consider the parametric equations x=t3-t,y=t3+t,t>0.

The objective is to analyze the direction of motion for the parametric equations.

Take the function x=t3-t.

Differentiate with respect to t.

Then, x1(t)=ddtt3-t

x1(t)=ddtt3-ddttx1(t)=3t2-1

Now take the function y=t3+t.

Differentiate with respect to t.

y'(t)=ddtt3+t

y'(t)=3t2+1

Thus, x1(t)>0and y1(t)>0.

Further the derivatives of the functions x(t),y(t)are increasing for the value of t.

As a result, the curve moves up and to the right in its motion.

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 Vaia!

One App. One Place for Learning.

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

Get started for free

Study anywhere. Anytime. Across all devices.

Sign-up for free