Advanced Math Archive: Questions from October 15, 2022
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1) \( x\left(x^{2}-y^{2}-x\right) d x-y\left(x^{2}-y^{2}\right) d y=0 \) 2) \( y\left(x^{2}+y\right) d x+x\left(x^{2}-2 y\right) d y=0 \) 3) \( y\left(x^{3} y^{3}+2 x^{2}-y\right) d x+x^{3}\left(x y^{2 answers -
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A) Find the local extrema of the functions \( f(x, y)= \) \( x+y, g(x, y)=x^{2}+y^{2} \), and \( h(x, y)=x^{3}+y^{3} \). B) Discuss the local extrema of the function \( k(x, y)=x^{n}+y^{n} \), where \2 answers -
2 answers
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solve by cauchy
\( \left\{\begin{array}{cr}x u_{x}+y u_{y}=2 u & (x, y) \in \mathbb{R} \\ u(1, y)=20 \cos (y) & y \in \mathbb{R}\end{array}\right. \)2 answers -
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The solution to the ED by sustitution is:
La solución de la ecuación diferencial \( \left(6 x^{2}-7 y^{2}\right) d x-14 x y d y=0 \), es: a. \( 2 x^{3}-7 y x^{2}=c \) b. \( 2 x^{3}+7 x y^{2}=c \) c. \( 2 x^{3}-7 x y^{2}=c \) d. \( 2 x^{3}+72 answers -
The solution to the ED is (x is the dependent variable):
La solución de la ecuación diferencial \( y \frac{d x}{d y}+x-\frac{x^{3} y}{2}=0 \), (x es la variable dependiente) es: a. \( x^{-2}=y+c y^{2} \) b. \( x^{-2}=2 y+c y^{2} \) с. \( x^{-2}=-y+c y^{22 answers -
I. Considere \( w=x^{2}-2 x y+y^{2}, x=r+\theta, y=r-\theta \) para determinar \( \frac{\partial w}{\partial r} \& \frac{\partial w}{\partial \theta} \). II. Considere \( w=x y \cos (z), x=t, y=t^{2}2 answers -
3) Graph each of the following functions. Find the period in each case. (i) \( \quad y=\sin \left(\frac{x}{2}\right) \). (ii) \( y=-|\cos (2 \pi x)| \). (iii) \( y=\sin \left(x+\frac{\pi}{2}\right) \)2 answers -
Resolver con explicación en palabras en casa ejercicio.
Instrucciones: Considere la gráfica dada para contestar las siguientes preguntas sobre las caracteristicas de la gráfica. Conteste todas las preguntas en el documento que debe entregar presentando l0 answers -
pictures below just in case for equation THERE IS A TRANSATION AND PICTURES BELOW. There is going to be a picture of part 1: Instructions are in the translation: Translation is in part 1!!!
TRANSLATION: 1. Taylor series theory: Taylor series are approximations of different functions by summations in the form of \( (\mathrm{x}-\mathrm{a})^{\prime \prime} \). This arises from the derivativ0 answers -
is it R with these operations a vector space over the rals? 2.,Determine if each set with the indicated operations is a vector space. If is not identify which property is NOT true. A. V= ((2,y) | 0
2. Ejemplos de Espacios Vectoriales 1. Sea \( \mathbb{V}=\mathbb{R}^{2} \). Defina \[ \begin{array}{c} \text { Suma } \\ (a, b)+(x, y)=(a+x, 0) \end{array} \] Multiplicacin por Escalar \[ t(x, y)=(t x2 answers -
2 answers
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( 1 point) Find \( y \) as a function of \( x \) if \[ y^{\prime \prime \prime}-2 y^{\prime \prime}-y^{\prime}+2 y=0 \] \[ \begin{array}{l} y(0)=-9, \quad y^{\prime}(0)=6, \quad y^{\prime \prime}(0)=32 answers -
( 1 point) Find \( y \) as a function of \( x \) if \[ \begin{array}{lc} y(0)=15, \quad y^{\prime}(0)=18, \quad y^{\prime \prime}(0)=4, \quad y^{\prime \prime \prime}(0)=0 \\ y(x)= \end{array} \]2 answers -
4. Solve the initial-value problem for the exact ordinary differential equation. \[ 2 x y-9 x^{2}+\left(2 y+x^{2}+1\right) y^{\prime}=0, \quad y(0)=-3 . \] A. \( y=\frac{-x^{2}-1+\sqrt{x^{4}+12 x^{3}+2 answers -
Determine the eigenvalues and eigenvectors of the following matrices
Determine los valores propios y vectores propios de las siguientes matrices: 1. \( \left[\begin{array}{rr}6 & -3 \\ -2 & 1\end{array}\right] \) 2. \( \left[\begin{array}{rrr}2 & -2 & 3 \\ 0 & 3 & -2 \2 answers