- #1

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## Homework Statement

Define f(0,0)=0 and f(x,y) = x

^{2}+y

^{2}-2x

^{2}y-4x

^{6}y

^{2}/(x

^{4}+y

^{2})

^{2}.

Show for all (x,y) that 4x

^{4}y

^{2}<=(x

^{4}+y

^{2})

^{2}and conclude that f is continuous.

## Homework Equations

## The Attempt at a Solution

Showing the inequality is trivial, but I do not see how I can conclude the function is continuous. I've done some messing around with the form of f, but am not getting anywhere.