求lim [sin(x^2-1)]/(x-1) x趋向于1的极限.
问题描述：
求lim [sin(x^2-1)]/(x-1) x趋向于1的极限.
答
lim(x→1) [sin(x^2-1)]/(x-1) = lim(x→1) {[sin(x^2-1)/(x^2-1)]×(x+1)}
=lim(x→1) [sin(x^2-1)/(x^2-1)]×lim(x→1) (x+1)
=1×(1+1)=2.