求极限lim(x-->正无穷)[(x+1)ln(x+1)-(x+1)lnx]

lim(x-->正无穷)[(x+1)ln(x+1)-(x+1)lnx]=lim(x-->正无穷)(x+1)[ln(x+1)-lnx]=lim(x-->正无穷)x[ln(x+1)-lnx]+lim(x-->正无穷)[ln(x+1)-lnx]=lim(x-->正无穷)x[ln(x+1)/x]+lim(x-->正无穷)[ln(x+1)/x]=lim(x-->正无穷)[ln(1+1/x)^x]+lim(x-->正无穷)[ln(1+1/x)]=lne+ln1=1