y=arctanx/x*x+1为有界函数
因为
|arctanx|<=π/2
0<=1/x^2<=1
所以|arctanx|/x^2<=π/2
从而
|y|=|arctanx/x*x+1|<=|arctanx/x*x|+1<=π/2+1
即有界π/2+1