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- - **How do I prove this multivariable limit problem?**
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How do I prove this multivariable limit problem?Compute $\displaystyle \lim_{x,y\to (0,0)}$ $\displaystyle 3xy\over x^2+y^3$ along lines of the form $\displaystyle y=mx$, for $\displaystyle m \neq 0$. What can you conclude? When I do it, I end up with 3m which is a limit. I know the function is discontinuous at (0,0) but I don't know how to prove it. |

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Actually, I get $\frac{3m}{1 + m^2}$ (valid for all $m$) by that approach, but the problem I identified before still applies. |

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