Question: finding values at which a limit exists/does not exist

I need to find where the limit of the function:

{1-cos(x*y^3)}/(x^2+y^6)^(1+a) exists/does not exists for different values of a, given 0<=a<=1 and as (x,y)->(0,0).

I've tried writing a procedure that changes a in particular increments but that is clearly not the most efficient way. Are there any rules of limits that I should be using?


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