Advanced Math Archive: Questions from April 15, 2023
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3. Find the vector lines of the vector field a.
3.1. \( \mathbf{a}=4 y \mathbf{i}-9 x \mathbf{j} \). 3.2. \( \mathbf{a}=2 y \mathbf{i}+3 x \mathbf{j} \). 3.3. \( \mathbf{a}=2 x \mathbf{i}+4 y \mathbf{j} \). 3.4. \( \mathbf{a}=x \mathbf{i}+3 y \math2 answers -
\( \begin{array}{l}y=4 x+5 \\ y=-0.25 x+3\end{array} \) \[ y=-0.25 x+3 \] a. Parallel b. Perpendicular c. Neither2 answers -
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6. \( y^{\prime \prime}=-y \) 7. \( y^{\prime}=\cosh 5.13 x \) 8. \( y^{\prime \prime \prime}=e^{-0.2 x} \)2 answers -
Find \( \frac{\partial z}{\partial x}, \frac{\partial z}{\partial y}, \frac{\partial^{2} z}{\partial x \partial y}, \frac{\partial^{2} z}{\partial x^{2}}, \frac{\partial^{2} z}{\partial y^{2}} \) and2 answers -
Verify Euler's for the following homogenous functions: a. \( f(x, y)=x^{2} y+x y^{2} \) b. \( f(x, y)=x^{4} y^{2}+x^{3} y^{3} \) C. \( f(x, y)=\frac{x^{4} y^{2}+x^{3} y^{3}}{x+y} \)2 answers -
Solve the initial value problem \[ y^{\prime \prime \prime}-4 y^{\prime \prime}+4 y^{\prime}=0 ; \quad y(0)=0, y^{\prime}(0)=1, y^{\prime \prime}(0)=2 \]2 answers -
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\[ 4 x^{2} y^{\prime \prime}+16 x y^{\prime}+9 y=0 \] Choose the right answer from the following possible answers: (a) \( y=\left[c_{1}+c_{2} \ln (x)\right] x^{\frac{3}{2}} \) (b) \( y=\left[c_{1}+c_{0 answers -
serie de fourier
Determine los desarrollos coseno y seno de semıntervalo para la tunción proporcionada. \[ f(x)=x^{2}+x, 02 answers -
Please solve.
GIVEN: \( \quad f: D \subset \mathbb{R}^{2} \longrightarrow \mathbb{R}, f(x, y)=\sin ^{2} x \cos y \) \[ \text { and } D=\left\{(x, y) \mid \begin{array}{ll} 0 \leq x \leq \frac{\pi}{2} \\ 0 \leq y \l2 answers -
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\[ \underline{g}(x, \underline{y}, z)=\frac{1}{\sqrt{x^{2} \pm y^{2} \pm z^{2}}}, \quad \underline{\forall}(x, \underline{y}, z) \in \mathbb{R}^{3} \backslash\{(0,0,0)\} \] Compute \( \Delta g(x, y, z2 answers -
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