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Chapter 6: Problem 56

Use a graphing utility to graph the curve represented by the parametric equations. Folium of Descartes: \(x=\frac{3 t}{1+t^{3}}, y=\frac{3 t^{2}}{1+t^{3}}\)

Short Answer

Expert verified
The plotted curve of the given parametric equations, the Folium of Descartes, displays a unique loop pattern with an asymptote.

Step by step solution

01

Identify the parametric equations

The given parametric equations are for the Folium of Descartes, which are given as \(x=\frac{3 t}{1+t^{3}}\) and \(y=\frac{3 t^{2}}{1+t^{3}}\). We will use a graphing tool to plot the curve represented by these equations.
02

Input the equations into the graphing utility

Next, input the parametric equations into the graphing utility. Most graphing tools allow you to input parametric equations directly.
03

Plot the curve

After the equations have been input, graph the curve by pressing the appropriate button or command on your graphing utility. Ensure the entire curve is visible by adjusting the viewing window if necessary.
04

Interpret the graph

Observe the graph. The Folium of Descartes is a special curve that looks like a loop and has an asymptote (a line that the curve approaches but never touches). Confirm that your graph has these characteristics.

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Most popular questions from this chapter

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