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Level Curvesby Grzegorz
Tags: curves 
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#1
Jan1910, 07:22 PM

P: 1

hi... I am new to this topic and frustrated.
I have a curve f(x,y)= 3y/(x^{2} +y^{2} + 1) I was asked to draw a level curve of this and I'm not getting anywhere with it. If anyone has any pointers, or can help me with solving this question I would be gretfull. The only other thing this question asks is to describe it at the orgin or at (0,3) ( which is steeper). thanks for any help. 


#2
Jan2010, 01:12 AM

P: 240

Level curves are curves where the function is constant, and equals lets say to a number c.
So you get an equation [tex]\frac{3y}{x^{2}+y^{2}+1}=c[/tex] Rearranging this gives you [tex]cx^{2}+cy^{2}3y=c[/tex] [tex]cx^{2}+cy^{2}2c\frac{3}{2c}y=c[/tex] [tex]cx^{2}+cy^{2}2c\frac{3}{2c}y+\frac{9}{4c^{2}}=\frac{9}{4c^{2}}c[/tex] [tex]cx^{2}+(cy\frac{3}{2c})^{2}=\frac{9}{4c^{2}}c[/tex] Now you just have to investigate different values of c. 


#3
Jan2010, 05:40 AM

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