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Advanced Math Archive: Questions from March 16, 2022

• a.Determine all potential critical points of the function. b. It employs a method to discriminate the above points. List the endpoints and saddle points.
  3. Considera la función f(x,y)= x + y -27x-12y. a. Determina todos los potenciales puntos críticos de la función. b. Emplea un método para discriminar los puntos anteriores. Enlista los extremos y
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• a. Find the linear approximation L(x,y) of the above function at the point (3,2). b. Use L(x,y) to approximate the value of (3.1, 2.2)f.
  4. Considera la función f(x,y)=r’- xy + y +3. a. Encuentra la aproximación lineal L(x,y) de la función anterior en el punto (3,2). b. Emplea L(x,y) para aproximar el valor de (3.1,2.2).
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• 1. - Prove that with the functional One can obtain the differential equation
  = 9 fi[rre 2 – 2nrpol dr se puede da obtener la ecuación diferencial e € do + +p= 0. r dr dr2 o d2 edh Ιω = ": [πεε(4β2 – 2πηρή α- ' J) 2 dr (dr da € dº dø E + + p = 0. = r d
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• A small circular hole is cut on one side of a large open tank. The hole is 4.1 m below the water level of the tank. Find the flow rate of the water in m/s (i.e. the rate at which the water comes out o
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  3. Let x, y E R be positive. Prove the following. (a) If x < y then x² < y2. (b) If x2 < y? then x < y. 1 1 (c) x < y if and only if х y (d) If x > 1 then x2 > x. (e) If x < 1 then x2 < x. ! α.
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  9. Let a, b E R with a < b. Prove the following. (a) If x, y € [a, b] then –(b − a) < x – y < b – a. (b) If x, y E (a,b) then –(b − a) < x - y
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  Usando multiplicadores de Lagrange verifique que el máximo y mínimo de f (x, y, z) = x/a +y/b+ z/c en la у elipsoide (x/a)2 + (y/b)2 +(z/c)2 = 1 son V3y - 3 respectivamente. =
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• Carry out the formal validity test of the following argument, using only the 19 rules of the image.
  1. ( AM).( XN) 2.2 (AVX) ::2 ( MN) 2.-4 1. P 2. 4 REGLAS DE INFERENCIA 1. Modus Ponens (M.P.) 2. Modus Tollens (M.T.) 3. Silogismo Hipotético (S. H.) 1. pag 1. paq 1. pag 2. P 2. qar ..9 -р .. par
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• Solve Laplace equation in the square Ω = {x, y | 0 < x, y < 1} with the boundary conditions u(x, 0) = sin πx, 0 < x < 1, u(x, 1) = 0, 0 < x < 1, u(0, y) = sin πy, 0 < y < 1
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  4. Let A ER"X" and ER". Compute dy/dx for the following. • y = xT A · y = xAx -
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  PARTE II. (TRANSPUESTA E INVERSA). 1. Halle la transpuesta de las matrices siguientes: 1 0 -1 2 b) -2 4 1 3 0 -7 c) 2 3 -1 0 0 2 2 1 -2 d) -3 0 5 0 -4 7 0 -1 1 0 3 e) 3 -4 2 f) 0 3 -2 - 3 2 0 7 -7 0 -
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  6.4 extra problems. El. Solve the IVP: V" - v' - 6y = e 'u(t) y(0) = 0, y'(0) = 1 E2. Solve the IVP: y" + 4y + 5y = tuz(t) y(0) = 0, y (0) = 0
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• need answer asap
  Find x and y. = x+2 4 -5 7 2y 2x 1-2 y + 2 2x + 6 4 -5 7 14 - 8 1-2 9 ♡ W (x, y) =
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• differential equations
  QUESTION 1 Resuelva la siguiente ecuación diferencial separable y responda las preguntas relacionadas Solve the separable differential equation and answer the related questions. dy *y Int (+1 A. ¿Cu
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