考研数学笔记 - 中值定理
in Math with 0 comment

考研数学笔记 - 中值定理

in Math with 0 comment

罗尔定理

$$
f_{\left( a \right)} = f_{\left( b \right)}
\; => \;
f_{\left( \xi \right)} = 0
$$

拉格朗日中值定理

$$
f_{\left( b \right)} - f_{\left( a \right)} = f_{\left( \xi \right)} \left( b - a \right)
$$

柯西中值定理

$$
\dfrac{f_{\left( b \right)} - f_{\left( a \right)}}{g_{\left( b \right)} - g_{\left( a \right)}} = \dfrac{f_{\left( \xi \right)}^\prime}{g_{\left( \xi \right)}^\prime}
$$

积分中值定理

$$
\int_{a}^b f_{\left( x \right)} g_{\left( x \right)} \, dx = f_{\left( \xi \right)} \int_{a}^b g_{\left( x \right)} \, dx
$$

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