grandes-ecoles 2021 Q29

grandes-ecoles · France · centrale-maths2__mp Not Maths Regularity and smoothness of transcendental functions

Let $\theta$ be the unique antiderivative of $\psi$ vanishing at 0. Show that $\theta$ is of class $\mathcal{C}^\infty$, constant on $]-\infty, -1]$ (we denote this constant by $A$) and constant on $[1, +\infty[$ (we denote this constant by $B$). Verify that $A \neq B$.

Let $\theta$ be the unique antiderivative of $\psi$ vanishing at 0. Show that $\theta$ is of class $\mathcal{C}^\infty$, constant on $]-\infty, -1]$ (we denote this constant by $A$) and constant on $[1, +\infty[$ (we denote this constant by $B$). Verify that $A \neq B$.

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