demo7.py

Created on January 11, 2022

389 Bytes

On démontre que lim (+inf)lnx=+inf 
Soit A qui appartient R+*, 
ln x>A <=> x>e^a 
car f(x)=e^x stt croissante
ainsi tout intervalle ]A;+inf[ 
  contient toutes les valeurs lnx 
  pour un x assez grand (ici x>e^x)
donc lim lnx =+inf


On demontre que lim (O+) lnx=-inf
on pose X=1/x donc 
lim x (0) = lim x (+inf)

ln x= ln 1/x = -ln X
Ainsi, lim (0) lnx=lim(+inf) - lnx=-inf

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