Question

lim[(x+2)/(x^2-1)]*sinx x趋向于无穷

Answer 1

先求lim[(x+2)/(x^2-1)]的极限,当x→∞,显然,lim(x+2)/(x^2-1)为0,即(x+2)/(x^2-1)为无穷小；
而sinx,当x→∞,极限不存在,由于sinx是个有界函数,根据：有界函数与无穷小的乘积仍然是无穷小,所以lim[(x+2)/(x^2-1)]*sinx=0