lim x→1 sin^2(x-1)/(x^2-1)的极限
问题描述：
lim x→1 sin^2(x-1)/(x^2-1)的极限
答
lim x→1 sin^2(x-1)/(x^2-1)
=lim x→1 sin(x-1)•sin(x-1)/[(x+1)•(x-1)]
=lim x→1sin(x-1)/(x-1)•lim x→1sin(x-1)/(x+1)
=lim x→1cos(x-1)/1•lim x→1sin(x-1)/(x+1)
=1•0
=0
这道题的技巧：利用极限运算规则：lim[f (x) g(x)] = limf (x) · limg(x)
然后再用洛必达法则.