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Soient Mathplace quicklatex.com-01c9bfbd63c15e710ed9bdd3694581cd_l3 Exercice 3  et Mathplace quicklatex.com-f87fdaff71b8bc3913ae3f27c24b34c5_l3 Exercice 3  les fonctions définies sur Mathplace quicklatex.com-4db59c8d8ef3d9383828a685b9e916cd_l3 Exercice 3  par Mathplace quicklatex.com-1d3c07f476ab8160ab508af520360410_l3 Exercice 3  et Mathplace quicklatex.com-4f957f14c53182697ae93e09624082ef_l3 Exercice 3  .

1- Etudier la Parité de Mathplace quicklatex.com-01c9bfbd63c15e710ed9bdd3694581cd_l3 Exercice 3  et de Mathplace quicklatex.com-f87fdaff71b8bc3913ae3f27c24b34c5_l3 Exercice 3  .

 

2-a) Calculer Mathplace quicklatex.com-3c30f62b1d660764c4715fcc114fd45c_l3 Exercice 3  et Mathplace quicklatex.com-a3f8022073ff56badfe8bebe44ce4dce_l3 Exercice 3  .

b) En utilisant des Propriétés de symetries, en déduire la valeur de Mathplace quicklatex.com-f7c4dc9971a4426770b9b06042d34d75_l3 Exercice 3  et Mathplace quicklatex.com-e0582ac77f598c1c4a3e245174abcd14_l3 Exercice 3  .

c) Calculer alors Mathplace quicklatex.com-afee05949de3e1f418d9da06b2e518ae_l3 Exercice 3  et Mathplace quicklatex.com-51c8c87d3a62b3cd3380dbee795cb618_l3 Exercice 3  .

 

 

 

 

1- On a Mathplace quicklatex.com-ea2ebe38aba5c0410f86d215c43e751f_l3 Exercice 3  donc Mathplace quicklatex.com-01c9bfbd63c15e710ed9bdd3694581cd_l3 Exercice 3  est paire

Mathplace quicklatex.com-f3ef96d22ede03e08a6fbd80321fea9c_l3 Exercice 3  donc Mathplace quicklatex.com-f87fdaff71b8bc3913ae3f27c24b34c5_l3 Exercice 3  est impaire

 

2- a) Mathplace quicklatex.com-2851b84ebf6aa239e473bde0945fffd1_l3 Exercice 3

Mathplace quicklatex.com-83ec76dbdfff318ebcecd0fcab12d550_l3 Exercice 3

 

b) Comme Mathplace quicklatex.com-01c9bfbd63c15e710ed9bdd3694581cd_l3 Exercice 3  est paire, par symetrie Mathplace quicklatex.com-49a34bee2364b6f9271ff4de15b003a6_l3 Exercice 3

Comme Mathplace quicklatex.com-f87fdaff71b8bc3913ae3f27c24b34c5_l3 Exercice 3  est impaire, Mathplace quicklatex.com-7d94a8a002762ce68fc2aaa3031374eb_l3 Exercice 3

 

c) D’après la relation de Chasles,

Mathplace quicklatex.com-6706ba1646af1e86a0c4ec5a478bb64c_l3 Exercice 3

Mathplace quicklatex.com-bbb92d47fe88d0f18c9648ab36e243c7_l3 Exercice 3