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differentiable_function [2016/01/23 19:06] nikolaj |
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=== Theorems === | === Theorems === | ||
- | Let $f(0)=0\neq f'(0)$, then | + | Let |
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+ | $f(0)=0\neq f'(0)$, | ||
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+ | then | ||
$\dfrac{ f(y\ f^{-1}(x)) }{y} =x+(y-1)\cdot\dfrac{f''(0)}{f'(0)^2}\cdot\dfrac{1}{2}x^2+{\mathcal O}(x^3)$ | $\dfrac{ f(y\ f^{-1}(x)) }{y} =x+(y-1)\cdot\dfrac{f''(0)}{f'(0)^2}\cdot\dfrac{1}{2}x^2+{\mathcal O}(x^3)$ |