Existence

[MMu]

Soit une fonction (réels).
Montrer q'il existe tels que
.

[beagle]

facile:

toujours en retard! - Page 4 2%29%3DA_n%24%20%285%29%20%5C%5C%20et%20en%20utilisant%20%28i%29%20%24A_n%24%20tend%20vers%20%24-%5Cinfty%24%20impossible%20car%20%24f%280%29%24%20est%20un%20nombre%20fixe

toujours en retard! - Page 4 Gif.latex?%24cas%203%20%3A%20%24f%281%29%3E0%24%20%5C%5Cdans%20%281%29%20on%20prend%20%24a%3D1%24%20et%20%24b%3D-n%24%20alors%20%5C%5C%20%24%5Cforall%20n%20%5Cin%20%5Cmathbb%20N%2C%20f%281-f%28-n%29%29%20%5Cleq%20f%28-n%29%5Ctimes%20f%281%29+1%24%20%286%29%20%5C%5Con%20pose%20%24a_n%3D1-f%28-n%29%24%20par%20%28i%29%20%24%5Clim%20a_n%3D+%5Cinfty%24%2C%20par%20%286%29%20%24%5Clim%20f%28a_n%29%3D-%5Cinfty%24%20%5C%5Cdans%20%282%29%20on%20prend%20%24b%3Da_n%24%20alors%20%24%5Cforall%20n%5Cin%5Cmathbb%20N%2Cf%280%29%20%5Cleq%20a_nf%28f%28a_n%29%29+f%28a_n%29%3DB_n%24%20%5C%5C%20impossible%20car%20la%20limite%20de%20%24B_n%24%20est%20%24-%5Cinfty%24%20et%20%24f%280%29%24%20nombre%20fixe

[MMu]

facile:

toujours en retard! - Page 4 2%29%3DA_n%24%20%285%29%20%5C%5C%20et%20en%20utilisant%20%28i%29%20%24A_n%24%20tend%20vers%20%24-%5Cinfty%24%20impossible%20car%20%24f%280%29%24%20est%20un%20nombre%20fixe

toujours en retard! - Page 4 Gif.latex?%24cas%203%20%3A%20%24f%281%29%3E0%24%20%5C%5Cdans%20%281%29%20on%20prend%20%24a%3D1%24%20et%20%24b%3D-n%24%20alors%20%5C%5C%20%24%5Cforall%20n%20%5Cin%20%5Cmathbb%20N%2C%20f%281-f%28-n%29%29%20%5Cleq%20f%28-n%29%5Ctimes%20f%281%29+1%24%20%286%29%20%5C%5Con%20pose%20%24a_n%3D1-f%28-n%29%24%20par%20%28i%29%20%24%5Clim%20a_n%3D+%5Cinfty%24%2C%20par%20%286%29%20%24%5Clim%20f%28a_n%29%3D-%5Cinfty%24%20%5C%5Cdans%20%282%29%20on%20prend%20%24b%3Da_n%24%20alors%20%24%5Cforall%20n%5Cin%5Cmathbb%20N%2Cf%280%29%20%5Cleq%20a_nf%28f%28a_n%29%29+f%28a_n%29%3DB_n%24%20%5C%5C%20impossible%20car%20la%20limite%20de%20%24B_n%24%20est%20%24-%5Cinfty%24%20et%20%24f%280%29%24%20nombre%20fixe

N'importe quoi ?

[beagle]

dis donc j'ai mis du temps à resoudre l'enigme,
c'est pas parce que je n'arrive pas le recopier qu'il faut m'insulter.

bon ok c'est pas vraiment de moi la réponse, ok, ok,
tu aimes les dattes?
https://palmeraie.forumactif.com/t26-existence

[MMu]

dis donc j'ai mis du temps à resoudre l'enigme,
c'est pas parce que je n'arrive pas le recopier qu'il faut m'insulter.

bon ok c'est pas vraiment de moi la réponse, ok, ok,
tu aimes les dattes?
https://palmeraie.forumactif.com/t26-existence

Tu ne sais pas copier !
Et bravo pour celle/celui qui a trouvé la solution