By Jacques Hadamard
Excerpt from Lectures on Cauchy's challenge in Linear Partial Differential Equations
Picard's researches - which we will quote of their position - also are crucial in different elements of the current paintings. Such can be the case for Le Roux.
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Extra info for Lectures on Cauchy's Problem in Linear Partial Differential Equations
Example text
1 Límite de una función MJTE DE U N A FU 75 N ( 1111�ideremos la funcíón f definida por la ecuación /(X) 2 2x + X x-1 t::: - 3 (1) 1 lhscrvemos quef(x) . cuando x 1,¡ l uncton se aproxime a 1 , pero no llega a ser igual a existe para toda x excepto x = 1 . Se investigará n los valores de 1 . El siguie nte ejemplo . tlmt rattvo muestra la forma en que podría obtenerse la funci ón definida por (1) y la 1 1116n por la cual se deben considerar dichos valor es de la función. • EJEMPLO 1 LUSTRATIVO 1 111 l'Cuación Y = 2x + x - 1 · ....
11 33. r) (a� �ot 1 está definida y (b) sec t no está def1111da. � 34. ) En los ejercidos 35 a 38, determine tan O cuantl� es el ángulo entre las rectas que tienen las pendlr tes dadas. }; (b) 4 Y -� 36. (a) t y -i; (b) t Y ! 37. (a) -t y �; (b) -1 Y -� 38. (a) - � y 2; (b) -t Y -+o 35. (a) 1 y lu� r�•ctas que tienen las ecuaciones 2x + tl O, 3x -y - 4 = O, y 3x + 4y + 8 = lunn redondeando a grados, las medidas lm 1\u¡¡ulos interiores del triángulo que tiene th 1� en ( 1 , 0), (-3, 2) y (2, 3).
Véase l a Figura 7 . fiGURA 8 Figu ra 8, o ... 51 y En la parte (d), nótese que, aun cuando x - 1 está definida para todos Jos valores de x, el dominio de g j, de acuerdo con la definición de función compuesta, es el con junto de todos los números x en el dominio dejpara los quej(x) está en el dominio de g. f. • Funciones ; (a) La función definida porj(x) = 5 es constante, tld eje x. (b) La función definida por g(x) = -4 es constante y su gráfica es una línea hori/Ontal 4 unidades por debajo del eje x.