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. lim_{(x,y)rightarrow(4,0)}x^2yln xy

Question
Limits and continuity
asked 2021-03-08
Use the method of your choice to evaluate the following limits.
\(\lim_{(x,y)\rightarrow(4,0)}x^2y\ln xy\)

Answers (1)

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.
0

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