Two variable limit

  • Thread starter gateman234
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  • #1
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Homework Statement


Lim [x^2*y^3/(x^4 + y^4)]
(x,y)->(0,0)
Find the limit or prove it doesn't exist

Homework Equations




The Attempt at a Solution


Tried considering the limit along the line x=y, and y=x^2, but couldnt show there where different vaules of limit for different curves. Then i graphed it, and it looked like the limit exists.
Attempted proof.
|x^2 y^3/(x^4 + y^4) - 0| < E
0< sqrt(x^2 + y^2)< d
this is where im stuck at.
 

Answers and Replies

  • #2
I like Serena
Homework Helper
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A simple way is to set e.g. y=0 and then solve it with x->0.

More generally you'd like to move from a general direction to the origin, because sometimes it matters where you're coming from (not in this case).
You can do that by substituting (x,y) = lambda (a,b) where a and b are not both zero.
Then you take the limit for lambda->0.
 

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