User:GFauxPas/Sandbox

Welcome to my sandbox, you are free to play here as long as you don't track sand onto the main wiki. --GFauxPas 09:28, 7 November 2011 (CST)

User:GFauxPas/Sandbox/Zeta2/lnxln1-x/existence

User:GFauxPas/Sandbox/Zeta2/lnxln1-x/integrand

User:GFauxPas/Sandbox/Zeta2/lnxln1-x/evaluation

User:GFauxPas/Sandbox/Zeta2/FourierSeries/

User:GFauxPas/Sandbox/Zeta2/Informal Proof

Theorem
Let $P_n: \R \to \R$ be a polynomial in $\R$ of degree $n$.

Then:


 * $\displaystyle \lim_{x \to +\infty} \frac {P_n\left({x}\right)}{\exp x} = 0$

Proof
By induction.

Theorem
Let:


 * $P_n\left({x}\right) = A_n x^n + A_{n-1} x^{n-1} + \cdots + A_1 x + A_0$

be a real polynomial of degree $n$.

Then:


 * $\displaystyle \lim_{x \to +\infty} = +\infty \, \text{or} \, -\infty$