Aruwin
Branch Unspecified
24 Jan 2012

# Leaf of Descartes

Someone,I need help in this.I have the answer but I can't think of a solution.I have tried a few things,though...

Parameterization of the leaf of Descartes.
y=tx => x= (3at)/(1+t^3)
y= (3at^2)/(1+t^3) (-infinity<t<infinity)

And here are some things I have figured out,
When t<-1,
t+1<0, 1+t^3<0 and hence x>0

When 0>t>-1,
t+1>0, 1+t^3>0 and hence x<0

*Here are the hints my teacher gave me:
limx(t-->-1)= +/- infinity
limx(t-->-1,t<-1)=infinity
limx(t-->-1,t>-1)= -infinity

and here is the answer:
7 years ago

Aruwin

Branch Unspecified
7 years ago
Praveen-Kumar
Yes,the graph and the table are the answer but i dunno the solution.

simplycoder

Branch Unspecified
7 years ago
Refer this, you would get the correct way atleast.
https://en.wikipedia.org/wiki/Folium_of_Descartes

Aruwin

Branch Unspecified
7 years ago
simplycoder
Refer this, you would get the correct way atleast.
https://en.wikipedia.org/wiki/Folium_of_Descartes
Sorry,I have read through it and I have got the idea.But how come the graph that my teacher drew is different than that that is shown on wikipedia?

Aruwin

Branch Unspecified
7 years ago
I am stucked now.
I have tried to differentiate dy/dx=(dy/dx)/(dx/dt) and I got [2t(1+t^3) - 3t^4]/(1-2t^3) but I am not sure if this is right or not.
So after I have differentiate this,what do I do next to make the graph table?

Aruwin

Branch Unspecified
7 years ago
Hey guys,it is alright.I have solved it myself 😀 I searched on the internet about descartes folium and studied it and then i got it 😀
7 years ago
Aruwin
Hey guys,it is alright.I have solved it myself 😀 I searched on the internet about descartes folium and studied it and then i got it 😀
Thats great... 😀

Dancer_Engineer

Branch Unspecified
7 years ago
Great! 😀