考研数学求极限题怎么做？

分子

√(1+x^2)= 1+(1/2)x^2 +o(x^2)

x+√(1+x^2)= 1+x+(1/2)x^2 +o(x^2)

ln[x+√(1+x^2)]

= ln[1+x+(1/2)x^2 +o(x^2)]

=[x+(1/2)x^2)]-(1/2)[x+(1/2)x^2]^2 +o(x^2)

=[x+(1/2)x^2)-(1/2)[x^2+o(x^2)]+o(x^2)

= x +o(x^2)

ln(1+x)= x -(1/2)x^2 +o(x^2)

ln(1+x)-ln[x+√(1+x^2)]=-(1/2)x^2 +o(x^2)？

分母

ln(x+√(1+x^2))= ln(1+x+o(x))= x+o(x)

ln(1+x) = x+o(x)

ln(1+x)。？ln(x+√(1+x^2)) =x^2 +o(x^2)

//

lim(x->；0)[1/ln(x+√(1+x^2))-1/ln(1+x)]

= lim(x->；0)[ln(1+x)-ln(x+√(1+x^2]]/[ln(x+√(1+x^2)).ln(1+x) ]

= lim(x->；0) -(1/2)x^2/x^2

=-1/2