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## Homework Statement

Find the limit, if it exists, or show that the limit does not exist.

[tex]lim_{(x,y)->(0,0)}[2x^{2}y/(x^4 + y^4)][/tex]

## Homework Equations

## The Attempt at a Solution

Along the y-axis and the x-axis, the limit approaches 0. Along y = mx, the limit also appaches 0. So, it appears that the limit is 0. However, the answer is that the limit "does not exist."

Should I just keep making new equations until I find where the limit does not = 0? I even tried the Squeeze Theorem...

0

__<__[tex][2x^{2}y/(x^4 + y^4)][/tex]

__<__[tex]2x^2[/tex]

because [tex]y/(x^4 + y^4)[/tex]

__<__1

so as x -> 0, the whole function -> 0 right?

Why doesn't that work to prove that the limit would be 0?

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