Differences
This shows you the differences between two versions of the page.
| Both sides previous revision Previous revision Next revision | Previous revision | ||
|
differentiable_function [2016/01/23 19:06] nikolaj |
differentiable_function [2016/01/23 19:07] nikolaj |
||
|---|---|---|---|
| Line 8: | Line 8: | ||
| ----- | ----- | ||
| === Theorems === | === Theorems === | ||
| - | Let $f(0)=0$, then | + | Let |
| + | |||
| + | $f(0)=0\neq f'(0)$, | ||
| + | |||
| + | then | ||
| $\dfrac{ f(y\ f^{-1}(x)) }{y} =x+(y-1)\cdot\dfrac{f''(0)}{f'(0)^2}\cdot\dfrac{1}{2}x^2+{\mathcal O}(x^3)$ | $\dfrac{ f(y\ f^{-1}(x)) }{y} =x+(y-1)\cdot\dfrac{f''(0)}{f'(0)^2}\cdot\dfrac{1}{2}x^2+{\mathcal O}(x^3)$ | ||
