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Advanced Math Archive: Questions from June 17, 2022

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  Q36: Let h(x)=√x + 2, g(x) = sin x - 3, then find the value of (goh)' (2) (hog)'(2) (sin 2)+1 (a) 2 (sin 4)-1 (b) 2 (c) (sin 2)-1 2 (d) √(sin 2) - 1
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• Find the pendants in directions of x and y in the point given. I need b.
  2. Encuentre las pendientes en las direcciones de r y y en el punto dado de las siguientes superficies. a. h(x, y) = 2x² - 3y², (1,1,-1). 30 plat b. z = sin(x) cos(y), (π/2, 0, 1) six con
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• 1. Determime the domain of the function and the set where is not continuous.
  1. Determinar el domininio de la función y el conjunto donde NO es continua. a. f(x,y) = +1 TY-1 b. f(x, y) xy²-x²y =
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  PRACTICE ANOTHER In(6x) 8x y' = 0 Need Help? MY NOTES Find y'. y = X Read It
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• Given the following subspaces of V = R4 S1 = {x ∈ R4 : x1 + x2 = x2 + x4 = 0} S2 = {x ∈ R4 : x1 − x4 = x3 + x4 = 0} a) Obtain a basis of the subspace A ∩ B b) Calculate S + T Is it direct sum?
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• What is the error in the following proof? If A is a complex matrix such that At = −A, so A is zero. Proof: Let J be the Jordan form of A, since At = −A then J t = −J implies that every element o
  6 ¿Cuál es el error en la siguiente demostración? Si A es una matriz compleja talque A¹ = − A, entonces A es cero. Demostración: Sea J la forma de Jordan de A, como At = -A entonces Jt = -J imp
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• Prove that the following matrix is ​​not diago- feasible and find an invertible matrix P which transforms the 3x3 matrix to its form Jordan canonical
  5 Prueba que la siguiente matriz no es diago- nalizable y encuentre una matriz invertible P que transforme la matriz de 3x3 a su forma canónica de Jordan 1 -1 3 (7) 0 2 1 0 0 2
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• Let T be a linear operator on the vector space V of dimension n and suppose that T has n distinct eigenvalues. Prove that T is diagonalizable
  4 Sea T un operador lineal sobre el espacio vec- torial V de dimension n y supongase que T tienen valores propios distintos. Demostrar que T es diagonalizable
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• Let x= [0,1]. Find the smallest sigma-algebra containing the sets:
  1. Sea X= [0,1]. Encuentra el o-álgebra más pequeña que contiene los conjuntos: [0,1/4), [1/4, 1/2), [1/2,3/4] y [3/4,1] (5pt)
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• Let F: X->Y. Let A be a phi-algebra en X and let B={ }. Prove that B is a phi-algebra.
  3. Sea f : XY. Sea A una o-álgebra en X y sea B = {E CY: f¹(E) E A}. Prueba que B es una σ-álgebra.
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  1.-(40 puntos) Considera el siguiente sistema de ecuaciones (2x+3y-z=3) 3x + y + z = 0 { y + 2z = 4 a) Define como A la matriz de coeficientes del sistema anterior y calcula su matriz de cofactores b)
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  A=6 B=4 C=3 find the solution of this differential equation using the parameter variation method Write the answer in the form y=f(x) completely simplify, coherent, complete, detailed and correct solut
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  A=6 B=4 C=3 Find the general solution of this initial value problem. write the answer in the form y= f(x) completely simplify, coherent, complete, detailed and correct solution.include all steps. Preg
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  Solve this initial value problem to express the displacement x of the mass as a function of time. interpret the resulting movement. Plot x(t). Pregunta 2 Resolver este PVI para expresar el desplazamie
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  A. 10. Which equation is not an identity? The aro length A. (1-tan²0)(1-cos² 0) = tan osin o tan o sin B. tan+sino tan sind C. D. = cos²x-sin²x cos²x+sinxcosx 1-cos y cos y sec y - 1 tan y tan y
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  14. Simplify coscos-sin sin 5 6 A. cos- 117 30 B. sin- 117 30 C. cos 30 T 30 D. sin-
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• Solve the differential equation by finding an integrating factor
  Resuelva la ecuación diferencial (6xy)dx+(4y+9x²) dy=0 encontrando un factor integrante (x,y) O. 15x³y² + 2y² = c 15x³y² + 2y² = c -3x²y²³ +2y² = c 3x²y³ + y² = c O Ninguna de las anter
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  Question 2 Utilice (x,y)=xy para convertir en exacta la ecuación (2ycos.x-xysinx) dx+2xcos.xdy=0. Utilice e criterio de exactitud para probar que la nueva ecuación es exacta. ƏM ƏN es exacta porqu
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• Match the left side to the right side.
  1. xy' = 2y 2. y' = 2 3. y' = 2y - 4 4. xy' = y 5. y" +9y = 18 6.xy" - y' = 0 a) y = 0 b) y = 2 c) y=2x d) y = 2x²
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• Find and equation of the tangent plane to the surface at the given point P.
  18 Hallar una ecuación del plano tangente a la superfiecie en el punto P dado. a. f(x, y) = P(1,2, 2) b. z = e(sin(y)+1), P(0,2,2) c. x² + 4y² + ² = 36, P(2, -2,4)
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• Please solve #10 by method of VOP
  [Exercise Set # 8] 1. y" + 3y" + 3y' + y = e-x-1 2. y" + 2y" - y' - 2y = 1 - 4x³ 8. yiv5y" + 4y = 10er, y" (0) = 0, y" (0) = 0 y(0) = 1, y'(0) = 0, 9. yiv y(0) = 1, y' + 5y" + 4y = 90 sin 4x. y" (0)
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  Draw a phase chart for the following first-order autonomous ODE: y' = (y - 3)(5 - y) (y — 2)
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