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**1. Homework Statement**

How can I show that the limit exists (or doesn't exist) for this function and prove it? I can't think of a function that will sandwich it to show it's 0 or a way to set x and y to make the limit not equal to zero! (oh and I'm trying to do all this without the use of delta epsilon methods!)

Thank you for all your help!

**2. Homework Equations**

lim as (x,y) goes to (0,0) for the function:

[(X^2)(Y^2)] / [X^4 + Y^2]

**3. The Attempt at a Solution**

I've tried looking at the limit by setting x and then y to zero and moving along each axis, which gives a limit of zero. So does using y=mx and approaching from a straight line. I've tried a couple of non-linear substitutions for y or x but it doesn't seem to get me anywhere. I guess that everything points to a limit of zero, but my problem is that you can only PROVE something does not have a limit by using the above methods and to PROVE that something has a specific limit then I believe that you require the sandwich rule and use 0 as the lower bound. Can anyone please help me with a function to use in the sandwich rule for this question?

Thanks for your help guys! :)