만약 x>1,증명:lnx>(2(x-1)/(x+1)

만약 x>1,증명:lnx>(2(x-1)/(x+1)

f(x)=lnx-2(x-1)/(x+1),f'(x)=1/x-[2(x+1)-2(x+1)]/(x+1)^2=1/x-4/(x+1)^2=[(x+1)^2-4x]/[x(x+1)^2]=(x-1)^2/[x(x+1)^2]>0,x>1 시,f(1)=0,그래서 f(x)>f(1)=0,즉 lnx>2(x+1)/(x+1)