# Limit of sequence of functions behaving strange

I'm trying to determine the limit of the sequence of functions

$$f_n(x)=\left(\frac{1}{\pi}\arctan(n x) + 1/2\right)^n.$$

I define

f[x_, n_] := (1/2 + ArcTan[n x]/Pi)^n

And enter

Limit[f[x, n], n -> Infinity]

Assuming[x > 0, Limit[f[x, n], n -> Infinity]]

I get the answer $$e^{-\frac{1}{x\pi}}.$$

While

Assuming[x < 0, Limit[f[x, n], n -> Infinity]]

Why does the normal Limit give the answer assuming that x<0? Is this a bug, or have I missed something?