grandes-ecoles 2012 QII.C.2

grandes-ecoles · France · centrale-maths1__mp Sequences and Series Convergence/Divergence Determination of Numerical Series

We define $$\varphi(x) = \begin{cases} \left(\frac{\sin x}{x}\right)^{2} & \text{if } x \neq 0 \\ 1 & \text{if } x = 0 \end{cases}$$ Justify that $\varphi \in L^{1}(\mathbb{R})$.

We define
$$\varphi(x) = \begin{cases} \left(\frac{\sin x}{x}\right)^{2} & \text{if } x \neq 0 \\ 1 & \text{if } x = 0 \end{cases}$$
Justify that $\varphi \in L^{1}(\mathbb{R})$.

Paper Questions

QI.A.1 QI.A.2 QI.A.3 QI.B.1 QI.B.2 QI.B.3 QI.B.4 QI.B.5 QI.C.1 QI.C.2 QI.C.3 QI.D.1 QI.D.2 QI.D.3 QI.D.4 QII.A QII.B.1 QII.B.2 QII.C.1 QII.C.2 QII.C.3 QII.D.1 QII.D.2 QIII.A.1 QIII.A.2 QIII.A.3 QIII.A.4 QIII.B.1 QIII.B.2 QIII.C.1 QIII.C.2 QIII.C.3 QIII.C.4 QIII.C.5 QIII.C.6 QIII.C.7