Advanced Math Archive: Questions from May 13, 2023
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1- Using the integrating factor to solve the following differential equations (a) \( y d x+\left(2 x-y e^{y}\right) d y=0 \), \( I(y)=y \) (b) \( (x+2) \sin y d x+x \cos y d y=0 \), \( I(x)=x e^{x} \)2 answers -
question 24,26,27
\( 23-28 \) = Find the absolute maximum and minimum values of \( f \) on the set \( D \). \( \begin{array}{l}f(x, y)=x^{2}+y^{2}+x^{2} y+4 \\ D=\{(x, y)|| x|\leqslant 1,| y \mid \leqslant 1\} \\ f(x,2 answers -
sea \( S \) el paraboloide \[ \begin{array}{c} \mathbf{F}(x, y, z)=y \mathbf{i}+2 z \mathbf{j}+x^{2} \mathbf{k}, \\ z=4-x^{2}-y^{2}, z \geq 0 . \end{array} \] a. Calcule curl \( \mathbf{F} \) b. Calcu2 answers -
que necesita para contestarlo?
sea \( S \) el paraboloide \[ \begin{array}{c} \mathbf{F}(x, y, z)=y \mathbf{i}+2 z \mathbf{j}+x^{2} \mathbf{k}, \\ z=4-x^{2}-y^{2}, z \geq 0 . \end{array} \] a. Calcule curl \( \mathbf{F} \) b. Calcu2 answers -
Solve a and b for the given problem
sea \( S \) el paraboloide a. Calcule curl \( \mathbf{F} \) b. Calcule la integral de superficie \( \iint_{\mathrm{S}} \operatorname{curl} F \cdot d S \), donde la parametrización de \( S \) es la ca2 answers -
Solve the two integral problems from the images
\[ \begin{array}{c} \mathbf{F}(x, y, z)=y \mathbf{i}+2 z \mathbf{j}+x^{2} \mathbf{k} \\ z=4-x^{2}-y^{2}, z \geq 0 \end{array} \] a. Calcule curl \( \mathbf{F} \) b. Calcule la integral de superficie \2 answers -
3. Sea y sea F(x, y, z)= xi + yj + zk, S = {(x, y, z): x² + y² + z² = 1}. Calcule la integral de superficie de F sobre S: //F 00 F.dS
\[ \begin{array}{c} \mathbf{F}(x, y, z)=x \mathbf{i}+y \mathbf{j}+z \mathbf{k}, \\ S=\left\{(x, y, z): x^{2}+y^{2}+z^{2}=1\right\} \end{array} \] Calcule la integral de superficie de \( \mathbf{F} \)2 answers -
5. Halla las dimensiones que maximizan el volumen de una caja con base cuadrada y área de superficie \( 10 \mathrm{~m}^{2} \) usando multiplicadores de Lagrange :2 answers -
Calculate the integral for the surface:
y sea \[ \mathbf{F}(x, y, z)=x \mathbf{i}+y \mathbf{j}+z \mathbf{k}, \] \[ S=\left\{(x, y, z): x^{2}+y^{2}+z^{2}=1\right\} \] Calcule la integral de superficie de \( \mathbf{F} \) sobre \( S \) : \[ \2 answers -
sea \( S \) el paraboloide \[ \begin{array}{c} \mathbf{F}(x, y, z)=y \mathbf{i}+2 z \mathbf{j}+x^{2} \mathbf{k}, \\ z=4-x^{2}-y^{2}, z \geq 0 . \end{array} \] a. Calcule curl \( \mathbf{F} \) b. Calcu2 answers -
\[ \begin{array}{l} \mathbf{F}(x, y, z)=x \mathbf{i}+y \mathbf{j}+z \mathbf{k}, \\ \text { y sea } \\ S=\left\{(x, y, z): x^{2}+y^{2}+z^{2}=1\right\} \\ \end{array} \] Calcule la integral de superfici2 answers -
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Let F(x,y,z) and let S, calculate the surface integral of F over S
\[ \begin{array}{c} \mathbf{F}(x, y, z)=x \mathbf{i}+y \mathbf{j}+z \mathbf{k}, \\ S=\left\{(x, y, z): x^{2}+y^{2}+z^{2}=1\right\} \end{array} \] Calcule la integral de superficie de \( \mathbf{F} \)2 answers -
Sea F(x,y,z) = yi+2zj+x^2k y sea S el paraboloide z=4-x^2-y^2, z> 0 a. Calcule curl F b. Calcule la integral de superfici
\[ \begin{array}{c} \mathbf{F}(x, y, z)=y \mathbf{i}+2 z \mathbf{j}+x^{2} \mathbf{k}, \\ z=4-x^{2}-y^{2}, z \geq 0 . \end{array} \] a. Calcule \( \operatorname{curl} \mathbf{F} \) b. Calcule la integr2 answers -
Sea F(x,y,z) = yi+2zj+x^2k y sea S el paraboloide z=4-x^2-y^2, z> 0 a. Calcule curl F b. Calcule la integral de superfici
\[ \begin{array}{c} \mathbf{F}(x, y, z)=y \mathbf{i}+2 z \mathbf{j}+x^{2} \mathbf{k}, \\ z=4-x^{2}-y^{2}, z \geq 0 . \end{array} \] a. Calcule \( \operatorname{curl} \mathbf{F} \) b. Calcule la integr2 answers -
\[ \begin{array}{c} \mathbf{F}(x, y, z)=x \mathbf{i}+y \mathbf{j}+z \mathbf{k}, \\ S=\left\{(x, y, z): x^{2}+y^{2}+z^{2}=1\right\} \end{array} \] Calcule la integral de superficie de \( \mathbf{F} \)2 answers -
Sea \[ \mathbf{F}(x, y, z)=x \mathbf{i}+y \mathbf{j}+z \mathbf{k} \] y sea \[ S=\left\{(x, y, z): x^{2}+y^{2}+z^{2}=1\right\} \] Calcule la integral de superficie de \( \mathbf{F} \) sobre \( S \) : \2 answers -
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1. Using the integrating factor to solve the following differential equations (a) \( y d x+\left(2 x-y e^{y}\right) d y=0 \), \( I(y)=y \) (b) \( (x+2) \sin y d x+x \cos y d y=0 \), \( I(x)=x e^{x} \)2 answers -
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Una empresa que se dedica a la producción de muebles y planifica producir sillas y mesas. Esto con los recursos disponibles, los cuales consisten en 800 pies de madera de caoba y 900 horas de mano de2 answers -
Una empresa petrolera tiene instalaciones de almacenamiento para combustible de calefacción en las ciudades A, B, C y D. Las ciudades C y D necesitan exactamente 500,000 galones de combustible. La co2 answers -
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