It's embarrassing, but we all know that Maxima does inf - inf --> 0.
Here Maxima does inf - inf --> 0 in the course of computing a limit.
What would happen to this limit problem if inf - inf --> und? Maybe
the limit would still evaluate correctly, I don't know.
(%i2) tlimit((x*atan(x))/(1+x),x,inf);
1> (SIMPLUS ((MPLUS) -1 ((RAT SIMP) 1 2)) 1 T)
<1 (SIMPLUS ((RAT SIMP) -1 2))
1> (SIMPLUS ((MPLUS) 1 $X) 1 NIL)
<1 (SIMPLUS ((MPLUS SIMP) 1 $X))
1> (SIMPLUS ((MPLUS) $INF ((MTIMES SIMP) -1 $INF)) 1 T)
<1 (SIMPLUS 0)
Barton