If I define the following: F[t_] := Sin[t]/t Then take the limit as t approaches 0: Limit[F[t], t -> 0]. It returns 1, but if I do this: F[0] It returns: Indeterminate. Is there a setting to automate limits? If not, would that be a good idea for a feature in a future Mathematica update? So that I can obtain 1 instead of Indeterminate from the function whose limit
F[t_] := Sin[t]/t
Limit[F[t], t -> 0]
F[0]
Indeterminate
Replacement rules, which behave according to syntax, are not the tool for this. 'Limit', which is intended for mathematical concepts, is a viable function for the purpose at hand. And it can handle more than just l'Hospital's rule types of examples.
Okay, thank you Daniel. I've known that this works, but thought that implementation of an automated "limit approacher" would be something that Mathematica users might find useful for such occasions.
There is an easy solution: Just define
f[0] = 1; f[0.] = 1.; f[t_] := Sin[t]/t
Remarks:
F
Sinc[]
I see your idea, but why not also have a built in way of getting F[0] without needing to define the same function at particular conditions? Something automated that will automatically provide the limit instead of indeterminate.
Well, there is the 'Sinc' function.
Again, not what I mean, I mean a setting for the generalized problem for: If there are two continuous and at least once differentiable functions (we'll call them F[t] and G[t], both are differentiable around the point c) such that F[c] = G[c] = 0 and that if I were to put F[c]/G[c] (or the reciprocal) that I shall automatically obtain the expected result F'[c]/G'[c] (or the reciprocal and however many times L'Hopital's rule must be applied) to obtain my desired answer instead of having Indeterminate returned as a result. I like having a broad fix for a single problem that can occur elsewhere. Another example: Find the slope of the function Sin[?*t]/Log[t] at t = 1
F[c] = G[c] = 0
