求lim(n->无穷)(3n+5)/(n^2+n+4)^1/2的极限

问题描述:

求lim(n->无穷)(3n+5)/(n^2+n+4)^1/2的极限

利用(1+1/n)^n在n趋于无穷极限为e。构造[1+(-6)/(3n^2+4)]^[(3n^2+4)/(-6)] 形式。结果为e^(-2) e^-2 点击图片可以

lim(n->无穷)(3n+5)/(n^2+n+4)^1/2=lim(n->无穷) (3n+5)/[ n(1+1/n+4/n^2)^(1/2)
= lim(n->无穷) (3+5/n)/(1+1/n+4/n^2)^(1/2)
= 3.