Mathematics 30 Online
OpenStudy (anonymous):

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

OpenStudy (anonymous):

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).

OpenStudy (anonymous):

ok yeah i get it, thanks spwolf21!