求极限:x[In(x+1)-Inx] x趋于正无穷答案1

问题描述:

求极限:x[In(x+1)-Inx] x趋于正无穷
答案1

lim(x趋近于+∞)【x^{In(x+1)-Inx}】
= lim(x趋近于+∞)【x^{In(x+1)/x}】
= lim(x趋近于+∞)【x^In(1+1/x)】
= lim(x趋近于+∞)【In(1+1/x)^x】
= ln e
= 1

1,In((x+1)/x)^x=In (1+1/X)^x=Ine=1

x[In(x+1)-Inx]
=x(ln(1+x)/x)
=x/ln(1+1/x) ln(1+1/x)~1/x
=x*1/x
=1