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?
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1 Answer
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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]*)
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$\begingroup$ Awesome! Thank you so much. $\endgroup$ Commented Feb 4, 2021 at 20:07
f /: Limit[f[z_], z_ -> 0, ___] := 0then all limits at0are0.{Limit[f[x], x -> 0], Limit[f[x], x -> 0, Direction -> "FromAbove"], Limit[f[x], x -> 0, Direction -> "FromBelow"], Limit[f[x], x -> 0, Direction -> "Reals"], Limit[f[x], x -> 0, Direction -> "TwoSided"], Limit[f[x], x -> 0, Direction -> 1], Limit[f[x], x -> 0, Direction -> -1], Limit[f[x], x -> 0, Direction -> "Complexes"]}$\endgroup$