I am not sure if power series would work!

Can we use power series to evaluate the limit of a multi-variable function?
I came up with the limit of (e^x-e^y)/(x-y) as (x,y) goes to (0,0) and thought about using power series expansion for e^x and e^y to help us evaluate the limit. We know both series have infinitely many terms but do they have the same amount of terms that allow us to do the factoring in the video? If you know the answer, please let me know. Thank you!

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