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

Question

Use the method of your choice to evaluate the following limits.

lim_{(x, y) \to (4, 0)} x^{2} y \ln x y

Answer 1

Given,
We have to evaluate the limit of $lim_{(x, y) \to (4, 0)} x^{2} y \ln x y$
Calculation,
Let, $y = m x$ , then
$lim_{x \to 4} x^{2} (m x) \ln x (m x) = lim_{x \to 4} m x^{3} \ln m x^{2} = 64 m \ln 16 m$
Since the limit is path-dependent. Hence the given limit does not exist.