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Proof: $1 = 0$

Let $x = 0$. Then,

$\displaystyle \frac{x}{x} = \frac{0}{x}$
$\displaystyle 1 = 0 \left({?}\right)$

Proof: $f \left({-x}\right) = f \left({x}\right) \implies f' \left({-x}\right) = -f' \left({x}\right)$

$\displaystyle \dfrac{\ \mathrm d {f \left({-x}\right)}}{\ \mathrm d x} = \dfrac{\ \mathrm d {f \left({x}\right)}}{\ \mathrm d x}$
$\displaystyle f' \left({-x}\right) = -f' \left({x}\right)$


I think you might want to explain that a little better. The notation is confusing at best. It may help to introduce an auxiliary function $g(x) = f(-x)$. --Dfeuer (talk) 18:19, 4 May 2013 (UTC)