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

Question
Limits and continuity
Use the method of your choice to evaluate the following limits.
$$\lim_{(x,y)\rightarrow(4,0)}x^2y\ln xy$$

2021-03-09
Given,
We have to evaluate the limit of $$\lim_{(x,y)\rightarrow(4,0)}x^2y\ln xy$$
Calculation,
Let, y=mx, then
$$\lim_{x\rightarrow4}x^2(mx)\ln x(mx)=\lim_{x\rightarrow4}mx^3\ln mx^2=64m\ln16m$$
Since the limit is path-dependent. Hence the given limit does not exist.

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