Answer to Question #107182 in Calculus for Nikesh gautam pandit ji

Question #107182
Check whether the function
f(x,y)= { 4x^2y/4x^4+y^2,. (x,y)not=to(0,0)
0 (x,y) = to (0,0)}

is continuous at ( 0,0).
1
Expert's answer
2020-04-02T06:36:12-0400

"\\lim\\limits_{(x;y)\\to (0;0)}\\frac{4x^2y}{4x^4+y^2}=[y=x^2]=\\\\=\\lim\\limits_{x\\to 0}\\frac{4x^2x^2}{4x^4+x^4}=\\frac{4}{5}\\ne0=f(0,0)"

Therefore the function "f(x,y)" is not continuous at ( 0,0).


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