(1)lim[(x+1)(x-2)]/[(x-1)(3x-1)]=1/2
问题描述:
(1)lim[(x+1)(x-2)]/[(x-1)(3x-1)]=1/2
(2)lim(2x+7)/[(x-1)(x+2)]=0
(3)lim(3x^2+2x+1)/[(3x+1)(3x-1)]=1/3
(4)lim(4x^2-4x+1)/(x^3+2x^2-2x+1)=0
(5)lim(1+2^2+3^2+……+n^2)/n^3=1/3
提示:1^2+2^2+3^2+……+n^2=n(n+1)(2n+1)/6
(6)lim(1+2+4+8+……+2^n)/2^n=1
请帮忙看看以上各式的解答是否正确,数学极限是我自学的,不知掌握的怎样,如有不对,还请指教,小女在此先谢谢了!
答
(1)lim[(x+1)(x-2)]/[(x-1)(3x-1)]=1/3
(6)lim(1+2+4+8+……+2^n)/2^n=lim [2^(n+1) - 1]/2^n=2
其他正确