   Chapter 10.1, Problem 30E

Chapter
Section
Textbook Problem

Graph the curves y = x3 − 4x and x = y3 − 4y and find their points of intersection correct to one decimal place.

To determine

To plot: The curve using the parametric equation y=x34x and x=y34y and find points of intersection.

Explanation

Substitute x=t in the equation y=x34x .

y=x34x=(t3)4(t)=t34t3

The parametric equation for the variable x1 is as follows.

x1=t (1)

The parametric equation for the variable y2 is as follows.

y2=x34x (2)

Calculation:

The value of t is increased from 3 to 3 with a step value of 1 and substituted in the parametric equations (1) and (2) to obtain the value of x and y, respectively.

Substitute 3 for t in equation (1),

x1=t3

Substitute 3 for t in equation (2),

y2=x34x=(3)34(3)=27+12=15

The values of x and y for each step value of t is tabulated in the below table.

 t −3 −2 −1 0 1 2 3 x −3 −2 −1 0 1 2 3 y −15 0 3 0 −3 0 15

Substitute y=t in the equation x=y34y .

x=y34y=(t)34(t)=t34t

The parametric equation for the variable x2 is as follows.

x2=t34t (3)

The parametric equation for the variable y2 is as follows.

y2=t (4)

The value of t is increased from 3 to 3 with a step value of 1 and substituted in the parametric equations (3) and (4) to obtain the value of x and y respectively

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