From the expression of limit function,

The first term of (1) limit function, when x→0, Arctan (1/0) = Arctan (∞) = π/2, so Xarctan (1/x) → 0; (2) the second term of the limit function is arctan x ~ x when x approaches infinity, so arctan x/x=x/x= 1.

Calculation process solution:

Function diagram From the function diagram, we can see that when x→0, y→- 1. That is, when x=0, y= 1.