I have implemented Newton's Method, and I am trying to find the exact value of the zero of a polynomial using `Limit`. The dream is that the following code works:

    g[x_] := 21 - 3 x - 7 x^2 + x^3;
    newtonNextGuess[f_, guess_] := guess - f[guess]/f'[guess];
    Limit[Nest[newtonNextGuess[g, #] &, 1, n], n -> Infinity]

But this returns an error:

    Nest: Non-negative machine-sized integer expected at position 3 in
        Nest[newtonNextGuess[g,#1]&,1,n].

The error persists if I make `n` an integer by replacing it with `1+Ceiling@Abs@n` as talked about in [this post](https://mathematica.stackexchange.com/questions/43932/limit-of-sequence). So the small question is: why is this error happening? But more importantly, is there way I can get Mathematica to tell me the limit of this sequence? The limit is $\sqrt{3}$, and it would be really nice to get Mathematica to display this explicitly (as opposed to numerically) for a presentation.