求下列函数极限：Limx•[1/e-(x/x+1)^x] x趋向于0

求下列函数极限：Limx•[1/e-(x/x+1)^x] x趋向于0
求下列函数极限：Limx•[1/e-(x/x+1)^x] x趋向于0

求下列函数极限：Limx•[1/e-(x/x+1)^x] x趋向于0
因为lim(x->0) (x/x+1)^x
=lim(x->0) [(1-1/(x+1))^(-(x+1))]^(-1)*(1-1/(x+1))^(-1)
=1/e
所以原式=0*0=0