Check whether the limit of the function
f(x,y)=3x^3y/x^6+2y^2 exists as (x, y) →(0,0)
1
Expert's answer
2020-03-30T09:55:30-0400
"\\lim_{x\\to\\ 0\\\\y\\to\\ 0}f(x,y)= \\frac{3\\frac{y}{x^3}}{1+2(\\frac{y}{x^3})^2}= \\frac{3k}{1+2k^2}" where "k=\\frac{y}{x^3}" .The limit "f(x,y)" depends on "k" hence "f(x,y)" has no limit.
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