# An algebra problem by Patrick Bourg

Algebra Level pending

Let $$f : [0,2015] \rightarrow \mathbb R$$ be the function defined as $f(x) = \frac{1}{1+x} \quad \forall x \in [0,2015].$

By the mean value theorem, one can show that $$\exists c_x \in (0,1)$$ such that :

$f(x) - f(0) = xf^{'}(xc_x), \quad \forall x \in [0,2015], \quad (exercise)$

What is : $$\lim_{x \rightarrow 0} c_x$$?

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