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December 13, 2023 -- a little late

In honor of Taylor Swift's 34's birthday, someone on FB posted 34 Taylor series!

They are lovely, but I've been out of it a while; what do they converge to??
DrWatson · 70-79, M
@ElwoodBlues It would take more time than I have right now to puzzle out each one, But the first is a^x and the last is e^x.

And I see that the guy goofed. Some of these are not Taylor series at all, in that they have leading terms that are not polynomial terms.
MartinTheFirst · 26-30, M
i could swear she'd be 50 by now, damn she ages slowly

 
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