Question

Check whether the function
f (x,y)=4x^2 y/4x^4+y^2, (x,y)≠(0,0)
0, (x,y)=(0,0)
is continuous at (0,0)

Answer 1

$\lim\limits_{x\to 0; y\to 0}\frac{4x^2y}{4x^4+y^2}=[\frac{0}{0}]=[y=x^2]=\lim\limits_{x\to 0}\frac{4x^4}{4x^4+x^4}= \frac{4}{5}\ne 0$

Therefore the function is not continuous at (0,0)