Can Limit take limits of unknown functions?

Question

For example, when I input this
 f[0] = 0;
Limit[f[x], x -> 0]

, it does not output 0.
Is there a way to get it to output 0 in this case?  For example, is there a way I can get Mathematica to assume f is continuous?

user64494 · Answer

Yes, it is possible.
ClearAll["Global`*"]; 
Limit[f[x], x -> 0,Analytic->True]
(*f[0]*)

Unfortunately,this option does not work for multidimensional limits, but works for iterated limits, e.g.
Limit[g[x, y], {x -> 1, y -> 0}, Analytic -> True]
(* g[1,0]*)

Can Limit take limits of unknown functions?

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