1.Lim(x→0)(1-x^2)^1/x2.lim(x→∞)(1+1/x-2)^x3.lim(x→+∞)(ln(1+x)-linx)/x现在就要答案,希望快回,

Question

1.Lim(x→0)(1-x^2)^1/x 2.lim(x→∞)(1+1/x-2)^x 3.lim(x→+∞)(ln(1+x)-linx)/x
现在就要答案,希望快回,

Answer 1

Lim(x→0)(1-x^2)^1/x=lim(x->0)e^(ln(1-x^2)/x)(用洛必达)=lime^(-2x/(1-x^2))=e^0=1lim(x→∞)(1+1/x-2)^x =lim(1+1/x-2)^(x-2)*x/x-2=e^(x/x-2)=elim(x→+∞)(ln(1+x)-lnx)/x(洛必达)=lim (1/1+x-1/x)=lim1/x(x+1...