Ayuda por favor. Sean f : R² - > R² y g : R³ - > R², dos campos vectoriales definidos por : f(x, y) = [[tex] e ^ {x + 2y} [ / tex], sen(y + 2x)], g(u, v, w) = (u + 2v² + 3w³, 2v - u²) a) Halle las diferenciales Df(x, y) y Dg(u, v, w) b) Halle la diferencial Dh(1, - 1, 1) para la función h(u, v, w) = f [g(u, v, w)].
En resumen
(a. 1) <img src="https://tex.z-dn.net/?
(a. 1)
<img src="https://tex.z-dn.net/?f=Df%28x%2Cy%29%3D%5Cleft%5B%5Cbegin%7Bmatrix%7D%0A%5Cnabla%28e%5E%7Bx%2B2y%7D%29%5C%5C%5Cnabla%5Csin%28y%2B2x%29%0A%5Cend%7Bmatrix%7D%5Cright%5D%5C%5C%20%5C%5C%20%5C%5C%0ADf%28x%2Cy%29%3D%5Cleft%5B%5Cbegin%7Bmatrix%7D%0Ae%5E%7Bx%2B2y%7D%262e%5E%7Bx%2B2y%7D%5C%5C2%5Ccos%28y%2B2x%29%26%5Ccos%28y%2B2x%29%0A%5Cend%7Bmatrix%7D%5Cright%5D%5C%5C%20%5C%5C%20%5C%5C" />
(a.
2)
<img src="https://tex.z-dn.net/?f=Dg%28u%2Cv%2Cw%29%3D%5Cleft%5B%5Cbegin%7Bmatrix%7D%0A%5Cnabla%28u%2B2v%5E2%2B3w%5E3%29%5C%5C%0A%5Cnabla%282v-u%5E2%29%0A%5Cend%7Bmatrix%7D%5Cright%5D%5C%5C%20%5C%5C%20%5C%5C%0ADg%28u%2Cv%2Cw%29%3D%5Cleft%5B%5Cbegin%7Bmatrix%7D%0A1%264v%269w%5E2%5C%5C%0A-2u%262%260%0A%5Cend%7Bmatrix%7D%5Cright%5D%5C%5C%20%5C%5C%20%5C%5C" />
(b)
<img src="https://tex.z-dn.net/?f=Dh%281%2C-1%2C1%29%3DJ_h%281%2C-1%2C1%29%3DJ_f%28g%281%2C-1%2C1%29%29%5Ccdot%20J_g%281%2C-1%2C1%29%5C%5C%20%5C%5C%20%5C%5C%0ADh%281%2C-1%2C1%29%3DJ_f%286%2C-3%29%5Ccdot%20J_g%281%2C-1%2C1%29%5C%5C%20%5C%5C%20%5C%5C%0ADh%281%2C-1%2C1%29%3D%5Cleft%5B%5Cbegin%7Bmatrix%7D%0A1%262%5C%5C%0A2%261%0A%5Cend%7Bmatrix%7D%5Cright%5D%0A%5Cleft%5B%5Cbegin%7Bmatrix%7D%0A1%26-4%269%5C%5C%0A-2%262%260%0A%5Cend%7Bmatrix%7D%5Cright%5D%5C%5C%20%5C%5C%20%5C%5C%0ADh%281%2C-1%2C1%29%3D%5Cleft%5B%5Cbegin%7Bmatrix%7D%0A-3%260%269%5C%5C%0A0%26-6%2618%0A%5Cend%7Bmatrix%7D%5Cright%5D%0A" />.
Si X es la media diferencial : 42 - X = X - 10 42 + 10 = X + X 52 = 2X X = 26.
En general : P. Aritmetica : a - b = c - d P. Geometrica : a / b = c / d Donde : . A - b = c - d (Cada termino es cuarta diferencial de los demas) . Media proporcional o geometrica : b = raiz cuadrada de ac . Halla la…
La media diferencial de 21 y 17 a = 21c = 127 a - b = b - c 21 - b = b - 17 21 + 17 = 2b 38 = 2b 19 = b : esa seria la media diferencial.