Question-208

Question Number 208 by 02@>@0 last updated on 25/Jan/15

Answered by 123456 last updated on 16/Dec/14

R andom things L O l I

lets f : [0 ∣ 1] \to R be a integable and continuos function

define ∥ f ∥ be [0 ∣ 1] \to R^{+} where

∥ f ∥= \sqrt{\underset{0}{\int^{1}} f^{2} d x}

wich we easy can check that

∥ c f ∥=∣ c ∣∥ f ∥

∥ f ∥⩾ 0

then if ∥ f ∥\neq 0, exist a vesor function given by

\hat{f} = \frac{f}{∥ f ∥}

Answered by 123456 last updated on 24/Dec/14

f_{n} (x) = \frac{x (x + 1) \cdot \cdot \cdot (x + n)}{x (x - 1) \cdot \cdot \cdot (x - n)}, n \in N

f = \lim_{n \to \infty} f_{n} (x) = ?

R \to R

z = {- 1, - 2, \dots, - n}

p = {0, + 1, + 2, \dots, + n}

f : N \times (R / p) \to R

f : n \times x \to f

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