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Special curves The following classical curves have been
Chapter 7, Problem 71AE(choose chapter or problem)
69-75. Special curves The following classical curves have been studied by generations of mathematicians. Use analytical methods (including implicit differentiation) and a graphing utility to graph the curves described by the following equations. Include as much detail as possible.
\(x^{3}+y^{3}=3 x y\) Folium of Descartes
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QUESTION:
69-75. Special curves The following classical curves have been studied by generations of mathematicians. Use analytical methods (including implicit differentiation) and a graphing utility to graph the curves described by the following equations. Include as much detail as possible.
\(x^{3}+y^{3}=3 x y\) Folium of Descartes
ANSWER:Solution 71AE Step1 Given equation 3 3 x +y = 3xy Step2 Differentiate the given equation implicitly we get d (x +y )= d 3xy dx dx 3x +3y 2 dy= 3y+3x dy dx dx (3y -3x) dy =3y-3x 2 2d