1
f(x)=1-e^(-x)f(x)-x/(x+1)=1-e^(-x)-[1-1/(x+1)] =1/(x+1)-e^(-x)0>x>-1时1/(x+1)=lim(n→∞) [1-(-x)^n]/[1-(-x)]=1+(-x)+(-x)^2+...+(-x)^ne^(-x)=1+(-x)+(-x)^2/2!+...(-x)^n/n!1/(x+1)>e^(-x)x=0时, 1/(x+1)=1=e^0x>0时, (x+1)e^(-x)所以x>-1时f(x)≥x/(x+1)
2
x≥0f(x)≥x/(ax+1)f(x)-x/(ax+1)≥0x/(ax+1)=1/a+ 1/[a(ax+1)]f(x)-x/(ax+1)=f(x)-[1/(x+1/a)]/ax=0时,f(x)=x/(ax+1)x>0时,f(ax)>ax/(ax+1)a≥1时, ax/(ax+1)≥ x/(ax+1), ax>x,1-e^(-x)>1-e^(-ax)a>1时,f(x)>f(ax)>x/(ax+1)a0,x=1/(1-a),x/(ax+1)=1, f(x)=1-e^(-x)