作业帮lim(x→л/2)cosx/(x-л/2)
来源：学生作业帮助网 编辑：作业帮 时间：2024/04/29 10:54:32
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lim(x→л/2)cosx/(x-л/2)
lim(x→л/2)cosx/(x-л/2)
lim(x→л/2)cosx/(x-л/2)
cosx=sin(л/2-x)
所以
原极限
=lim(x→л/2) sin(л/2-x) /(x-л/2)
=lim(x→л/2) -sin(x-л/2) /(x-л/2)
那么x→л/2的时候,x-л/2趋于0,
所以由重要极限lim(x→0) sinx /x=1可以知道,
原极限
=lim(x→л/2) -sin(x-л/2) /(x-л/2)
= -1
或者用洛必达法则,对分子分母同时求导,
得到
原极限
=lim(x→л/2) sin(л/2-x)' /(x-л/2)'
=lim(x→л/2) -cos(л/2-x) / 1
= -cos0
= -1
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