Advanced Math Archive: Questions from October 18, 2022
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Consider the function. \[ f(x, y)=6 x^{2} y^{3} \] (a) Find \( \int_{0}^{3} f(x, y) d x \). (b) Find \( \int_{0}^{1} f(x, y) d y \).2 answers -
Evaluate the double integral. \[ \iint_{D} 5 x \sqrt{y^{2}-x^{2}} d A, D=\{(x, y) \mid 0 \leq y \leq 2,0 \leq x \leq y\} \]2 answers -
Solve following questions (Exact function) (1) \( (2 x y+1) d x+\left(x^{2}-2\right) d y=0 \); (2) \( \left(e^{2 x}+3 y\right) d x+(3 x-\sin y) d y=0 \) \( (3) \) \( (\sin y-y \sin x) d x+(\cos x+x \c2 answers -
[9 pts.] Cierto o False. Detennina si los siguientes enunciados son ciertos of falsos. 1. Se puede decir que \( y=x^{5} \) es solución de la ecuación differencial \( x^{2} y^{\prime \prime}-7 x y^{\2 answers -
[9 pts.] Cierto o Falso. Determina si los siguientes enunciados son ciertos o falsos. 1. Se puede decir que \( y=x^{5} \) es solución de la ecuación diferencial \( x^{2} y^{\prime \prime}-7 x y^{\pr2 answers -
Canonic hiperbolic
\( U_{\eta \eta}^{\prime \prime}+U_{\xi \xi}^{\prime \prime}-\frac{1}{\eta} U_{\eta}^{\prime} \mathrm{v}=0 \) \( \xi=y \quad \eta=2 \sqrt{x} \)2 answers -
Solve the next Separable Differential Equations
Resolver las siguientes ecuaciones diferenciales separables: a) \( \frac{d y}{d x}=\frac{x^{2}-1}{y^{2}} \) b) \( \frac{d y}{d x}=3 x^{2} y \)2 answers -
Solve the next Homogeneous Differential Equations
Resolver las siguientes ecuaciones diferenciales homogéneas: a) \( \frac{d y}{d x}=-\frac{\left(x^{2}+y^{2}\right)}{2 x y} \) b) \( \frac{d y}{d x}=\frac{x y-y^{2}}{x^{2}} \)2 answers -
2. Find the inverse Laplace transform of the following. \[ H(s)=\frac{s \mathrm{e}^{-4 s}}{(3 s+2)(s-2)} \] Q 3. Solve \( \quad \frac{d^{2} y}{d t^{2}}-3 \frac{d y}{d t}+2 y=2 e^{-1}, y^{(0)}=2, \qua2 answers -
[3 pt] 19. Select the logical expression that is equivalent to: \( \neg \forall x \exists y(P(x) \wedge Q(x, y)) \) a. \( \exists x \forall y(\neg P(x) \vee \neg Q(x, y)) \) b. \( \exists y \forall x(2 answers -
Encuentre \( L\left\{e^{2 t-1}\right\} \) \[ x-(2 t-1) \] \[ \frac{1}{e(s-2)} \] \[ \frac{2}{s-e} \] Ninguna de las anteriores2 answers -
2 answers
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2 answers
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5. Solve the IVP. \( y^{\prime \prime}-y^{\prime}-12 y=0, y(0)=3, y^{\prime}(0)=5 \) Answer: \( y=2 e^{4 x}+e^{3 x} \)2 answers -
(1 point) Solve the equation \( y^{\prime \prime}+100 y=e^{2 x} \) where \( y(0)=y^{\prime}(0)=0 \). \( y(x)= \)2 answers -
(1 point) Solve the equation \( y^{\prime \prime}+196 y=e^{2 x} \) where \( y(0)=y^{\prime}(0)=0 \). \[ y(x)= \]2 answers -
question 12 hw 5
Given \( f(x, y, z)=-e^{6 x y z} \) \[ f_{x}(x, y, z)= \] \[ f_{y}(x, y, z)= \] \[ f_{z}(x, y, z)= \]2 answers -
2 answers
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2 answers
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complete using power series please
\( y^{\prime \prime}+2 \sin x y=0 \) \( y^{\prime}+\exp (-x) y=0 \) \( \left(x^{\wedge} 2+1\right) y^{\prime \prime}+2 y^{\prime}=0 \)0 answers -
Consider the two planes π1:5x+4y+6z=14 Y π2:−5x+6y+z=23. If ℓ is the line where π1 and π2 intersect, and v⃗ is a direction vector of ℓ of the form v⃗ =(β,−35,γ), we can state that th
Considere los dos planos \( \pi_{1}: 5 x+4 y+6 z=14 \) \( y \) \( \pi_{2}:-5 x+6 y+z=23 \). Si \( \ell \) es la recta donde se intersecan \( \pi_{1} \) y \( \pi_{2} \), y \( \vec{v} \) es un vector di2 answers