Notes in 06常用不等式

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Published	10/05/2024	常用不等式1设a，b为实数，则\(\|a \pm b\| \leqslant\text{______}\),\(\|\| a\|-\| b\|\| \leqslant\text{______.}\)
Published	10/05/2024	常用不等式2\(\text{______}\leqslant \frac{a+b}{2} \leqslant\text{______.}\)
Published	10/05/2024	常用不等式3\(\text { 设 } a>b>0, \text { 则 }\left\{\begin{array}{l}\text { 当 } n>0 \text { 时, } a^{n}>\text{______,} \\\text { 当 } n<0 \…
Published	10/05/2024	常用不等式4\(\text { 若 } 0<a<x<b, 0<c<y<d \text {, 则 }\) \(\text{______}<\frac{y}{x}<\text{______.}\)
Published	10/05/2024	常用不等式5当\(\left(0<x<\frac{\pi}{2}\right)\) ，\(sinx \text{______}x \text{______}tanx\)
Published	10/05/2024	常用不等式6当\((0 \leqslant x \leqslant 1)\)， \(\arctan x\text{______}x \text{______}\arcsin x(0\leqslant x \leqslant 1)\)
Published	10/05/2024	常用不等式7\((\forall x)\) \(\mathrm{e}^{x}\)\(\text{______}\)\(x+1\)
Published	10/05/2024	常用不等式8当x>0，\(x-1\text{______}lnx\)
Published	10/05/2024	常用不等式9对于\(x>0，\)\(\text{______}<\ln \left(1+\frac{1}{x}\right)<\text{______}\)
Published	10/05/2024	常用不等式10问\(x \in\left(0, \frac{\pi}{2}\right)\)，判断 \(\frac{2}{\pi}x\text{______}x\)\(\text{______}\) \(sinx\)之间的大小关系
Published	10/05/2024	常用不等式11\(x \in\left(0, \frac{\pi}{4}\right)\) \(x\)\(\text{______}\)\(tanx\)\(\text{______}\)\(\frac{4}{\pi} x\)
Published	10/05/2024	常用不等式12\(\begin{array}{c} 调和平均值  H_{n}=\frac{n}{\sum \limits_{i=1}^{n}\frac{1}{x_{i}}}= \frac{n}{\frac{1}{x_{1}}+ \frac{1}{x_{2}}+ \cdots + \frac…
Published	10/05/2024	常用不等式表格  ①设a，b为实数，则\(\|a \pm b\| \leqslant\text{______}\),\(\|\| a\|-\| b\|\| \leqslant\text{______.}\) ②\(\text{______}\leqslant \frac{a+b}{2} \leq…
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