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Advanced Math Archive: Questions from September 11, 2022

• number 2 please
  Q3) Find the solution of the initial value problems: 1) \( y^{\prime}-y=2 \cos 5 t, \quad y(0)=0 \) 2) \( y^{\prime \prime}-5 y^{\prime}+4 y=0, \quad y(0)=1, \quad y^{\prime}(0)=0 \) 3) \( y^{\prime \
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  4. Classify the critical points of \( f(x, y)=\left(x^{2}-y^{2}\right)\left((x-1)^{2}+y^{2}\right) \).
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  Find \( x_{1} y, \theta_{2}, \theta_{3} \) \( x^{2}+\left(y^{2}-5\right)^{2}=16 \) \( x=1 \sin 60+5.2 \sin \theta_{2}+1.5 \cos \left(\theta_{3}-270\right) \) \( y=1 \cos 60+5.2 \cos \theta_{2}+2.5 \si
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• True or false If f(x) and g(x) are analytic functions on X0, then h (x)=f (x)/g (x) is also analytics at X0 I need an explanation of why it is true or false f(x) and g(x) have this form
  Si f \( (x) \) y g \( (x) \) son funciones analíticas en \( x 0 \), entonces \( h(x)=f(x) / g(x) \) también es analítica en \( x 0 \) (1 Punto) \( f(x)=\sum_{n=0}^{\infty} a_{n}\left(x-x_{0}\right
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  analize the continuity of the function II. Analice la continuidad de la función a) \( f(x, y, z)=\frac{z}{x^{2}+y^{2}-4} \) b) \( f(x, y)=\left\{\begin{array}{c}\frac{\operatorname{sen}(x y)}{x y}, x
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• A = {x ∈ R : x = y 3 + y 2 + y for some y ∈ Q}. Prove that A ⊆ Q.
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  5. Use a table to express the values of each of these Boolean functions. a) \( F(x, y, z)=\bar{x} y \) b) \( F(x, y, z)=x+y z \) c) \( F(x, y, z)=x \bar{y}+\overline{(x y z)} \) d) \( F(x, y, z)=x(y z
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  Let \( \mathbf{x}=\langle-1,-2\rangle, \mathbf{y}=\langle-5,-1\rangle \), and \( \mathbf{z}=\langle 15,12\rangle \). If possible, find a nontrivial integer solution: \[ \langle 0,0\rangle=\quad \mathb
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  Find the solution of the initial-value problem: \[ x y^{\prime}+y=6 x e^{x}, y(-3)=7 \mathrm{e}^{-3} . \] a) \( y=6 x e^{x}-6 e^{x}-3 \mathrm{e}^{-3} \) b) \( y=6 x e^{x}-6 x^{-1} e^{x}+3 \mathrm{e}^{
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• La solucion de la ecuacion diferencial dada es:
  La solución de la ecuación diferencial \( x d y=2(y-\sqrt[2]{x y}) d x \), es: a. \( \quad 16 x y=\left(y+4 x+c x^{2}\right)^{2} \) b. \( \quad 16 x y=\left(y-4 x-c x^{2}\right)^{2} \) c. \( 16 x y=
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  Find the general solution of \[ y^{\prime}=\frac{2 x\left(y^{2}-16\right)}{x^{2}+2} \] a) \( y=\frac{4-4\left(x^{2}+2\right)^{2}}{1+\left(x^{2}+2\right)^{2}} \) b) \( y=\frac{4+4\left(x^{2}+2\right)^{
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• please help
  (1 point) Perform the following integrations: 1) \( y^{\prime}=2 e^{2 x} \sin \left(e^{2 x}\right) \Rightarrow y= \) 2) \( y^{\prime}=\frac{x+5}{x^{2}+10 x+10} \Rightarrow y= \) 3) \( y^{\prime}=\cos
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  Solve the separable initial value problem. 1. \( y^{\prime}=\ln (x)\left(1+y^{2}\right), y(1)=0 \Rightarrow y= \) 2. \( y^{\prime}=6 x \sqrt{1+x^{2}}\left(1+y^{2}\right), y(0)=1 \Rightarrow y= \)
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  Solve the separable initial value problem. \( 1 . \) \( y^{\prime}=6 x \sqrt{1+x^{2}\left(1+y^{2}\right), y(0)=4 \Rightarrow y=} \) \( 2 . \) \[ y^{\prime}=\ln (x)\left(1+y^{2}\right), y(1)=4 \Rightar
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