My goal is to understand how Mathematica computes limits that would require differentiability assumptions on functions (for, for instance, L'Hopital or Taylor Series). Consider, for instance, the following limit:

Limit[ n * (F[x - 1/Sqrt[n]] + F[x + 1/Sqrt[n]] - 2 F[x]), 
 n -> Infinity] 

If F is a smooth (or just a C^2) function, this should converge to F''(x) by Taylor expansion. Is it possible to define assumptions on F[x] as a smooth function, so that Mathematica would be able to evaluate the above limit?


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