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Chapter 9: Q.5 (page 721)

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

x=t2,y=t3,t鈭�鈩�

Short Answer

Expert verified

As a consequence, the curve's motion is up and to the right when t>0, and up and to the left when t<0

For this reason, the correct answer is up and to the left.t<0,up and to the right when t>0.

Step by step solution

01

Given information

Consider the equations that are parametric.x=t2,y=t3,t鈭�鈩�

02

calculation

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

Take the functionx=t2

Differentiate with respect tot.

Thenlocalid="1653373572829" width="93">x1(t)=ddtt2=2tx'(t)>0

03

further calculation

Now take the function y=t3

Differentiate with respect to t

y'(t)=ddx3t2=6ty1(t)=6t>0

Thus, x'(t)>0and y'(t)>0.

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