问一道极限的问题若lim(an^3+bn^2+2)/(2n^2+2n+1)=1,求a和b的值

Question

问一道极限的问题
若lim (an^3+bn^2+2)/(2n^2+2n+1)=1,求a和b的值

Answer 1

lim (an³+bn²+2)/(2n²+2n+1)
=lim an³/(2n²+2n+1) + lim (bn²+2)/(2n²+2n+1)
=lim an/[2+(2/n)+(1/n²)] + lim [b+(2/n²)]/[2+(2/n)+(1/n²)]
=lim an/[2+(2/n)+(1/n²)] + b/2
若a≠0,则lim an/[2+(2/n)+(1/n²)]趋于无穷大,与题目条件极限存在不符合
所以a=0,b/2=1
a=0,b=2