# Homework Help: Limit in several variables

1. May 12, 2013

### manjum423

Evaluate the limit or prove that it does not exist..

f(x,y) -> (0,0)
3xy/((x^2)+(4y^2))

The attempt at a solution:

Set x to 0 and you get 0
set y to 0 and you get 0
set y=x and you get 3x^2/5x^2 = 3/5
This means that limit does not exist.

Is this correct?
If this is correct, how do you know that you have to set y=x? Is there a generic approach to these kinds of problems?
Thank you for taking the time to read this and for your help.

2. May 12, 2013

### tiny-tim

welcome to pf!

hi manjum423! welcome to pf!

(try using the X2 button just above the Reply box )
completely
you try y = kx first (for constant k),

if that doesn't work, try y = kxn

if that doesn't work, assume the limit exists, and try to prove it!

alternatively, use polar-ish coordinates, eg x = 2rcosθ, y = rsinθ, giving … ?

3. May 12, 2013

### SammyS

Staff Emeritus
Hello manjum423 . Welcome to PF !

We do like you to use the supplied homework template.
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

You seem to have some difficulty writing you problem. It appears that you problem is something like:
Evaluate the limit or prove that it does not exist..

Lim(x,y)→(0,0) 3xy/((x2)+(4y2))

Which can be displayed more nicely using LaTeX.

$\displaystyle \lim_{(x,y)\to(0,0)} \frac{3xy}{(x^2)+(4y^2)}$