Numerador
√(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)?
Denominador
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)
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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