求极限：lim((2n∧2-3n+1)/n+1)×sin n趋于无穷

Question

求极限：lim((2n∧2-3n+1)/n+1)×sin<1/n> n趋于无穷

Answer 1

lim【n→∞】(2n²-3n+1)/(n+1)×sin(1/n)
=lim【n→∞】(2n²-3n+1)/(n+1)×(1/n)
=lim【n→∞】(2n²-3n+1)/(n²+n)
=lim【n→∞】(2-3/n+1/n²)/(1+1/n)
=(2-0+0)/(1+0)
=2
答案：2