用泰勒级数和等价无穷小,令t=1/x,求t->0时候的极限即可,此时分母=e^(t)-1->t分子ln(x+√(x^2+1))-ln(x+√(x^2-1))=lnx+ln(1+√1+(1/x^2))-[lnx+ln(1+√1-(1/x^2))]=ln(1+√1+(1/x^2))-ln(1+√1-(1/x^2))=ln(1+√(1+t...