求极限lim{n[ln(n+1)-lnn] n→∞求极限lim{n[ln(n+1)-lnn] n→∞lim(x^3+x^2)/(x-2)^2 x→2limx^2sin1/x^2 x→0
问题描述：
求极限lim{n[ln(n+1)-lnn] n→∞
求极限
lim{n[ln(n+1)-lnn] n→∞
lim(x^3+x^2)/(x-2)^2 x→2
limx^2sin1/x^2 x→0
答
① 等价无穷小量替换：ln(1+t) t (t->0)lim(n→∞) n[ln(n+1)-lnn] =lim(n→∞) nln[(n+1)/n]=lim(n→∞) nln(1+1/n)=lim(n→∞) n*(1/n)=1② ∵ lim( x→2) (x^3+x^2) = 12 ; lim( x→2) 1/(x-2)^2 = +∞lim( x→2)...