Relatively easy limit help please

  • Thread starter Hessam
  • Start date
  • #1
36
0
ok... so i'm taking calc3, and didnt go to class for a month, lol

now i can't solve this (what seems like) a simple limit... please help


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?

thankyou very much in advance
 
Last edited:

Answers and Replies

  • #2
92
0
The limit does not exist

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

[tex]x=y=z[/tex] and [tex]x=y=-z[/tex]

You'll find [tex]\frac {3x^2} {3x^2}[/tex] and [tex]\frac {-x^2} {3x^2}[/tex]

Whose limits are 1 and [tex]-\frac {1} {3}[/tex], which are different. CVD
 

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