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Questions about the function Assuming[], the $Assumptions system variable, and the Assumptions option of functions such as Simplify[] and Integrate[].

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Can Limit take limits of unknown functions?

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 …