考研数学笔记 —— 中值定理
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考研数学笔记 —— 中值定理

in 高数 with 0 comment, Views is 55

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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