In calculus we use taylor series expansion at large number of places.I recently one of the application in number theory(To find solution of polynomial in finite field of order $p^{n}$, where p is prime and n is some natural number). I didnt understand why the procedure should work here except that it works here(i solved some problems based on this procedure).
So are there any other places where we can use the taylor approximation and also its limitations(if any).
