grandes-ecoles 2012 QIV.B

grandes-ecoles · France · centrale-maths1__psi Sequences and Series Evaluation of a Finite or Infinite Sum
In this part, $\lambda(t) = t$ for all $t \in \mathbb{R}^+$.
In the particular case where $f(t) = e^{-at}t^n$ for all $t \in \mathbb{R}^+$, with $n \in \mathbb{N}$ and $a \in \mathbb{R}$, make explicit $E$, $E^{\prime}$ and calculate $Lf(x)$ for $x \in E^{\prime}$. 
In this part, $\lambda(t) = t$ for all $t \in \mathbb{R}^+$.

In the particular case where $f(t) = e^{-at}t^n$ for all $t \in \mathbb{R}^+$, with $n \in \mathbb{N}$ and $a \in \mathbb{R}$, make explicit $E$, $E^{\prime}$ and calculate $Lf(x)$ for $x \in E^{\prime}$.
Paper Questions
QI.A QI.B QI.C QII.A QII.B QII.C QIII.A QIII.B QIII.C QIII.D QIV.A QIV.B QIV.C QIV.D QV.A QV.B QV.C QV.D QV.E QV.F QV.G QVI.A QVI.B QVI.C QVII.A QVII.B QVIII.A QVIII.B QVIII.C QVIII.D QVIII.E QVIII.F QVIII.G