grandes-ecoles 2025 Q38

grandes-ecoles · France · centrale-maths2__official Proof Deduction or Consequence from Prior Results
In this subsection, we assume that $J_n = J_n^{(\mathrm{C})}$, the matrix introduced in subsection A-II.
We set $G_h : x \longmapsto \frac{(x-h)^2}{2\beta} - \ln(2\operatorname{ch}(x))$.
Deduce that $\psi$ is differentiable on $\mathbb{R}_+^*$ and that $m(h) = \frac{u(h) - h}{\beta}$ for all $h \in \mathbb{R}_+^*$. 
In this subsection, we assume that $J_n = J_n^{(\mathrm{C})}$, the matrix introduced in subsection A-II.

We set $G_h : x \longmapsto \frac{(x-h)^2}{2\beta} - \ln(2\operatorname{ch}(x))$.

Deduce that $\psi$ is differentiable on $\mathbb{R}_+^*$ and that $m(h) = \frac{u(h) - h}{\beta}$ for all $h \in \mathbb{R}_+^*$.
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