grandes-ecoles 2016 QIII.E.1

grandes-ecoles · France · centrale-maths1__pc Reduction Formulae Determine Asymptotic Behavior or Limits of Sequences Defined by Integrals

We assume $\lambda < 1$. Determine $\lim_{n \rightarrow +\infty} \left((n\lambda)^{-n} \int_{0}^{n\lambda} (n\lambda - t)^{n} \mathrm{e}^{t} \mathrm{~d}t\right)$.

We assume $\lambda < 1$. Determine $\lim_{n \rightarrow +\infty} \left((n\lambda)^{-n} \int_{0}^{n\lambda} (n\lambda - t)^{n} \mathrm{e}^{t} \mathrm{~d}t\right)$.

Paper Questions

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