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@@ -38,7 +38,7 @@ |
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\end{salign*} |
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Ist $m = 1$, so gilt: |
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\begin{salign*} |
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f(x+h) - f(x) &= \int_{0}^{1} \sum_{i=1}^{n} \pdv{f}{x_{i}}(x+sh) \d{s} \cdot h_{i} = \sum_{i=1}^{n} \left( \int_{0}^{1} \pdv{f_{i}}{x_{i}}(x+sh) \d{s} \right) \cdot h_{i} \\ &= \left( \int_{0}^{1} \nabla f(x+sh) \d{s}, h\right)_{2} |
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f(x+h) - f(x) &= \int_{0}^{1} \sum_{i=1}^{n} \pdv{f}{x_{i}}(x+sh) \d{s} \cdot h_{i} = \sum_{i=1}^{n} \left( \int_{0}^{1} \pdv{f}{x_{i}}(x+sh) \d{s} \right) \cdot h_{i} \\ &= \left( \int_{0}^{1} \nabla f(x+sh) \d{s}, h\right)_{2} |
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\end{salign*} |
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Ist $m \geq 2$, so gilt analog zu oben: |
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\begin{salign*} |
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