求limx→∞[x(π/2-arctanx)

问题描述:

求limx→∞[x(π/2-arctanx)

lim[x(π/2-arctanx)]
=lim[(π/2-arctanx)/(1/x)]
=lim[-1/(1+x^2)/(-1/x^2)]
=lim[x^2/(1+x^2)]
=1