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## Homework Statement

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

Stewarts Calculus 7th edition 14.2 Q13.

## Homework Equations

## The Attempt at a Solution

[itex]f(x,y)=\frac{xy}{\sqrt{x^{2}+y^{2}}}[/itex]

The limit along any line through (0,0) is 0, as well as along other

paths through (0,0) such as [itex]x=y^{2}[/itex] and [itex]y=x^{2}[/itex]

Let [itex]\epsilon>0[/itex] We want to find [itex]\delta>0[/itex] such that

if [itex]0<\sqrt{x^{2}+y^{2}}<\delta[/itex] then [itex]\left|\frac{xy}{\sqrt{x^{2}+y^{2}}}-0\right|<\epsilon[/itex]

Edit: Still can't get the latex working

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