函数f(x)等于x-Sinx在R上的零点有多少个?急用哦
人气:246 ℃ 时间:2019-08-20 09:09:32
解答
零点即是g(x)=x和h(x)=sinx的交点
g(x)和h(x)都过(0,0)
g(x)斜率1
g'(x)=cosx
g'(0)=1
∴g(x)和h(x)在原点相切
当x<0时,h(x)始终在g(x)上方
当x>0时,h(x)始终在g(x)下方
所以只有一个交点(0,0)
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