lim x趋近于1求sin(x的平方-1)/(x-1)
问题描述：
lim x趋近于1求sin(x的平方-1)/(x-1)
答
把分母也化为x平方-1
该极限就变成了x平方-1趋近于0的极限计算了。答案为2
答
lim [sin(x^2-1)]/(x-1)
= lim (x+1)[sin(x^2-1)]/(x^2-1)
= lim (x+1)
= 2
答
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