# Relatively easy limit help please

#### Hessam

ok... so i'm taking calc3, and didnt go to class for a month, lol

lim
(x,y,z) -> (0,0,0)

of this

xy + yz + zx
-----------------
(x^2)+(y^2)+(z^2)

i tried doing the limit as (x,y,z) approaches (x,0,0) (0,y,0) and (0,0,z) and got zero, but that's not the answer

however when i put it into my calc and grind it out i get 1... but how can i do it on paper?

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#### Maxos

The limit does not exist

To show that, take two curves, e.g:

$$x=y=z$$ and $$x=y=-z$$

You'll find $$\frac {3x^2} {3x^2}$$ and $$\frac {-x^2} {3x^2}$$

Whose limits are 1 and $$-\frac {1} {3}$$, which are different. CVD

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