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lim x→1 sin^2(x-1)/(x^2-1)的极限

来源:学生作业帮 编辑:作业帮 分类:数学作业 时间:2024/10/05 03:54:50
lim x→1 sin^2(x-1)/(x^2-1)的极限
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.