[(x+2)ln(x+2)-2(x+1)ln(x+1)+xln(x)]*x x趋向于正无穷,求它的极限.怎么解,答案是1_数学解答

[(x+2)ln(x+2)-2(x+1)ln(x+1)+xln(x)]*x x趋向于正无穷,求它的极限.怎么解,答案是1

人气：372 ℃　时间：2020-05-19 07:31:28

解答

(x->+∞)lim[(x+2)ln(x+2)-2(x+1)ln(x+1)+xln(x)]*x=(x->+∞)[(x+2)ln(x+2)-2(x+1)ln(x+1)+xln(x)]/(1/x),【为0/0型】用罗比达法则=(x->+∞)-[ln(x+2)+1-2ln(x+1)-2+ln(x)+1]/(1/x^2),=(x->+∞)lim-[ln(x+2)-2ln(x+1...