Hello everyone, This problem is bugging me because the professor showed me this is how you do it, the day before the exam, so what do i do? well I do it the way he told me, and I totally miss it. Here is the problem: I'm going to let f(x) be the function to make it easier to read: f(x) = [xy+yz+zx]/[x^2+y^2+z^2]; Lim f(x); (x,y,z)->(0,0,0) So I let Lim f(x); (x,y,z)->(t,3t,0) and i got: (xy)/(x^2+y^2) = (t)(3t)/(t^2+(3t)^2) = 3t^2/10^2 = 3/10; Lim f(x); (x,y,z)->(0,3t,t) yz/(y^2+z^2) = (3t)(t)/((3t)^2+t^2)) = 3/10; Lim f(x); (x,y,z)->(t,0,3t) zx/(x^2+z^2) = 3/10; So I said the limit exists because they all go to 3/10, and yet he marked it wrong. Any ideas why this is wrong? Thanks. He's saying the limit doesn't exist.