x趋向于无穷大时lim(1+k/x)^x =e^lim(x->∞)ln(1+k/x)/(1/x) 令1/x=t,则t->0 原式=e^lim(t->0)ln(1+kt)/t =e^lim(t->0)k/(1+kt)/1 =e^k
