show that lim(x,y)-(0,0) y^2/(x^2+y^2) does not exist?
i know i can set y = mx and show that the limit is dependent on m, but how do i go about doing this?
show that lim(x,y)-(0,0) y^2/(x^2+y^2) does not exist?
i know i can set y = mx and show that the limit is dependent on m, but how do i go about doing this?
@Mathematics

Question

show that lim(x,y)->(0,0)  y^2/(x^2+y^2)   does not exist?
i  know i can set y = mx and show that the limit is dependent on m, but how do i go about doing this?
 show that lim(x,y)->(0,0)  y^2/(x^2+y^2)   does not exist?
i  know i can set y = mx and show that the limit is dependent on m, but how do i go about doing this?
 @Mathematics

anonymous · Answer

If you set y=mx, $$ \lim_{(x,y) \rightarrow (0,0)} f(x,y)=m ^{2}/1+m ^{2}$$
This limit changes with each value of the slope m. So there is no single number you may call the limit of f(x,y).

anonymous · Answer

ok yeah i get it, thanks spwolf21!