求lim [sin(x^2-1)]/(x-1)x趨向於1的極限.

求lim [sin(x^2-1)]/(x-1)x趨向於1的極限.

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.