求极限：limx→∞[（x-12）2-x4ln2（1+1x）]．

Question

求极限：

lim

x→∞

[（x-(1)/(2)）²-x⁴ln²（1+(1)/(x)）]．

Answer 1

由题意可知：limx→∞[(x−12)2−x4ln2(1+1x)]=limx→∞{(x−12)2−[x2ln(1+1x)]2}，x2ln(1+1x)＝x2(1x−121x2+131x3−141x4+o(1x4))=(x−12)+131x−141x2+o(1x2)，(x−12)2−x4ln2(1+1x)=−2(x−12)(131x−141x2+o(...