P005练习

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# P005练习 试证 Jordan 不等式: \begin\{aligned\} \frac\{2\}\{\pi\}x < \sin x < x\quad \left(0 < x < \frac\{\pi\}\{2\}\right). \tiny\boxed\{\begin\{array\}\{c\}\mbox\{跟锦数学微信公众号\}\\\\\mbox\{zhangzujin.cn\}\end\{array\}\}\end\{aligned\} [购书](https://mp.weixin.qq.com/s/9RUc7PhEAjT7vlZk4lqZSw) / [答疑](https://mp.weixin.qq.com/s/JGYZG5rsshf7Z2Amo2di8A) / [pdf1](https://mbd.pub/o/zhangzujin) / [pdf2](https://mbd.pub/o/gjsx) / \begin\{aligned\} &f(x)=\frac\{\sin x\}\{x\}\\\\ \Rightarrow&f'(x)=\frac\{x\cos x-\sin x\}\{x^2\} =\frac\{x-\tan x\}\{x^2\sec x\} < 0\left(\mbox\{单位上画图\}\right)\\\\ \Rightarrow&\forall\ 0 < x < \frac\{\pi\}\{2\},\ \frac\{2\}\{\pi\}=f\left(\frac\{\pi\}\{2\}\right) < f(x) < f(0+)=1. \tiny\boxed\{\begin\{array\}\{c\}\mbox\{跟锦数学微信公众号\}\\\\\mbox\{zhangzujin.cn\}\end\{array\}\}\end\{aligned\} 跟锦数学微信公众号. [在线资料](https://mp.weixin.qq.com/s/F-TU-uzeo3EjxI5LzjUvRw) / [公众号](https://mp.weixin.qq.com/s/pdC49P5WZXTEpRBa0JBfow) / [资料目录](https://mbd.pub/o/bread/mbd-YpiZmJdv) / [视频](https://space.bilibili.com/507709073) / [微信群](https://mbd.pub/o/bread/mbd-YZmTkp1w)