# Use the method of your choice to evaluate the following limits. lim_{(x,y)rightarrow(4,0)}x^2yln xy

Use the method of your choice to evaluate the following limits.
$\underset{\left(x,y\right)\to \left(4,0\right)}{lim}{x}^{2}y\mathrm{ln}xy$
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Given,
We have to evaluate the limit of $\underset{\left(x,y\right)\to \left(4,0\right)}{lim}{x}^{2}y\mathrm{ln}xy$
Calculation,
Let, $y=mx$, then
$\underset{x\to 4}{lim}{x}^{2}\left(mx\right)\mathrm{ln}x\left(mx\right)=\underset{x\to 4}{lim}m{x}^{3}\mathrm{ln}m{x}^{2}=64m\mathrm{ln}16m$
Since the limit is path-dependent. Hence the given limit does not exist.

Jeffrey Jordon