(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

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. Relevant 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! :)

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# Homework Help: Proving this limit

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