diff options
Diffstat (limited to 'notes/Sep-15.org')
| -rw-r--r-- | notes/Sep-15.org | 8 |
1 files changed, 4 insertions, 4 deletions
diff --git a/notes/Sep-15.org b/notes/Sep-15.org index d5bf371..8a64089 100644 --- a/notes/Sep-15.org +++ b/notes/Sep-15.org @@ -36,11 +36,11 @@ Again, $f'(a) \approx \frac{f(a+h) - f(a)}{h}$, $e = |\frac{1}{2} f''(a) + \frac{1}{3!}h^2 f'''(a) + \cdots$ -$R_2 = \frac{h}{2} f''(u)$ +$R_2 = \frac{h}{2} f''(\xi)$ -$|\frac{h}{2} f''(u)| \leq M h^1$ +$|\frac{h}{2} f''(\xi)| \leq M h^1$ -$M = \frac{1}{2}|f'(u)|$ +$M = \frac{1}{2}|f'(\xi)|$ *** Another approximation @@ -48,5 +48,5 @@ $\text{err} = |f'(a) - \frac{f(a) - f(a - h)}{h}|$ $= f'(a) - \frac{1}{h}(f(a) - (f(a) + f'(a)(a - (a - h)) + \frac{1}{2}f''(a)(a-(a-h))^2 + \cdots))$ -$= |f'(a) - \frac{1}{h}(f'(a) + \frac{1}{2}f''(a)h)|$ +$= |f'(a) - (f'(a) + \frac{1}{2}f''(a)h)|$ |