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:(adsbygoogle = window.adsbygoogle || []).push({});

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.

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# Homework Help: Limit as (x,y,z)->0, I missed it on the exam but why?

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