- #1
mr_coffee
- 1,629
- 1
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.
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.