TD_5 - x 2 + xy + y 2 si ( x,y ) 6 = (0 , 0) si ( x,y ) =...

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TRAVAIL DIRIG ´ E 5 Mohammed Saddoune AUTOMNE 2009 Question 1 : Dressez un diagramme de courbes de: a) f ( x,y ) = x 3 - y b) f ( x,y ) = e y/x c) f ( x,y ) = y x 2 + y 2 . Question 2 : Dire si la limite existe et, si oui, calculer sa valeur: a) lim ( x,y ) (0 , 0) x 2 sin 2 y x 2 + y 4 b) lim ( x,y ) (0 , 0) xy 4 x 2 + y 8 . c) lim ( x,y ) (0 , 0) x 3 + y 3 x 2 + y 2 Question 3 : eterminer le plus grand domaine sur lequel la fonction: f ( x,y ) = xy
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Unformatted text preview: x 2 + xy + y 2 si ( x,y ) 6 = (0 , 0) si ( x,y ) = (0 , 0) est continue. 1 Question 4 : Ecrire lexpression de h ( x,y ) = g ( f ( x,y )) et d eterminez lensemble sur lequel la fonc-tion est continue: g ( t ) = t-1 t + 1 et f ( x,y ) = x 2-y. M.SADDOUNE 2...
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TD_5 - x 2 + xy + y 2 si ( x,y ) 6 = (0 , 0) si ( x,y ) =...

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