limita

[cristinat]

lim x->oo din ln(1+2x+x^3) / ln(1+3x). cum aplic limita lim x->0 ln(1+x)/x aici??

[DD]

Limita este de tipul ∞/∞si putem aplica L^' Hospital.deci L=(ln(1+2x+x^3 ) )^'/ln(1+3x)^' =lim(x→∞)((2+3x^2)/(1+2x+x^3 ))*((1+3x)/3)=
Lim(x->∞) x^3*(2/x^2+3)*(1/x+3)/(x^3*3*(1/x^3+2/x^2+1))->3

[cristinat]

Limita este de tipul ∞/∞si putem aplica L^' Hospital.deci L=(ln(1+2x+x^3 ) )^'/ln(1+3x)^' =lim(x→∞)((2+3x^2)/(1+2x+x^3 ))*((1+3x)/3)=
Lim(x->∞) x^3*(2/x^2+3)*(1/x+3)/(x^3*3*(1/x^3+2/x^2+1))->3

fara l'Hospital va rog

[DD]

lim(x->inf)[{ln(x^3.(1/x^3+2/x^2+1)}/{ln(x(1/x+3)}]=lim(x->inf)[(3.lnx+
ln(1/x^3+2/x^2+1))/(ln3.x+ln(1/3x+1))=lim(x=>inf)[3lnx/ln(3x)]=lim(x=>
inf)[3lnx/(lnx.(1+3/lnx)]-->3

[gigelmarga]

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