Originally Posted by

**iva** I have some problems where I need to determine if the limits exist using the limit definition or limit laws. For the following 2 I think i can use the laws but would like to make sure:

$\displaystyle lim

](x,y)-> (0,0) = y/x^2$

Make y approach zero along the line $\displaystyle y=x$ and then it follows

at once that the limit doesn't exist.

Tonio

I used the product rule splitting into 2 ie

$\displaystyle f(x,y) = y$ and $\displaystyle g(x,y) = 1/x^2 $

This would give a limit of 0 times infinity = 0 respectively right?

Then the 2nd problem I thought I could handle the same way ie:

$\displaystyle lim

(x,y)-> (1,0) y/x, $

I thought i could solve it the same way, ie use the product rule with 2 equations f(x,y)=y and g(x,y) = 1/x giving

$\displaystyle lim

(x,y) -> (1,0) f(x,y) g(x,y) = (0)(1) = 0. $

I still need to do the proofs now but would like to know if i''m on the right track in terms of at least getting the limits right?

many thanks!