lim x趋近于1求sin(x的平方-1)/(x-1)

题目

lim x趋近于1求sin(x的平方-1)/(x-1)

答案

1).是0/0型用罗必塔法则作!
lim x→1[sin(x^2-1)/(x-1)] =lim x→1[2xcos(x^2-1)]=2
2)用两个重要极限作
lim [sin(x^2-1)]/(x-1)----------------------分子分母同乘x+1
= lim (x+1)[sin(x^2-1)]/(x^2-1)
= lim (x+1)
= 2