作业帮求极限lim(x-->0) (tanX-sinX)/[(sin^3)X]
来源：学生作业帮助网 编辑：作业帮 时间：2024/04/27 15:28:34
![求极限lim(x-->0) (tanX-sinX)/[(sin^3)X]](/uploads/image/z/1697302-46-2.jpg?t=%E6%B1%82%E6%9E%81%E9%99%90lim%28x--%3E0%29+%28tanX-sinX%29%2F%5B%28sin%5E3%29X%5D)
求极限lim(x-->0) (tanX-sinX)/[(sin^3)X]
求极限lim(x-->0) (tanX-sinX)/[(sin^3)X]
求极限lim(x-->0) (tanX-sinX)/[(sin^3)X]
(tanx-sinx)/sin³x
=(sinx/cosx-sinx)/sin³x
=(1/cosx-1)/sin²x
=[(1-cosx)/cosx]/(1-cos²x)
=1/[cosx(1+cosx)]
所以极限=1/[1*(1+1)]=1/2