Calculus Archive: Questions from May 03, 2023
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For block Ω in Oxyz space bounded by curved surfacesand Find the correct equality c.Another answer Just the correct answer, no explanation needed. I am ch
\( y=x^{2}, y=4, z=0, z=x \) \( I=\iiint_{\Omega} f(x, y, z) \mathrm{d} V \) a. \( I=\int_{-2}^{0} \int_{x^{2}}^{4} \int_{x}^{0} f(x, y, z) \mathrm{d} z \mathrm{~d} y \mathrm{~d} x+\int_{0}^{2} \int2 answers -
Differentiate with respect to \( x \). Exurcae: 1. \( y=\frac{x}{x+\sin x} \) 2. \( y=\frac{x+\sin x}{1+\cos x} \) 3. \( y=\frac{x^{3}+3 x}{(x+1)(x-2)} \) 4. \( y=\frac{x^{2} \sin x}{(x+1)\left(x^{2}-2 answers -
2. Find the general solutions of the following ODEs: (a) \( y^{\prime \prime}-6 y^{\prime}+9 y=18 x \) (b) \( y^{\prime \prime}-6 y^{\prime}+9 y=-e^{3 x} \) (c) \( y^{\prime \prime}-6 y^{\prime}+9 y=12 answers -
Q9) \( \lim _{x \rightarrow 0^{+}} 3 x \sin \frac{2}{x}= \) c) \( k=0 \) d) \( \mathrm{k}=0, \frac{1}{2} \) Q10) \( \lim _{x^{2}-3 x} \) b) \( \frac{1}{2} \) c) 0 d) \( \frac{2}{3} \)2 answers -
Find the general solution of the differential equation \[ y^{\prime}+3 x^{2} y=12 x^{2} \] \[ y=4+C e^{-x^{3}}, C \in \mathbb{R} \] \[ y=-1+C e^{-x^{3}}, C \in \mathbb{R} \] \[ y=1+C e^{-x^{3}}, C \in2 answers -
Find the general solution of the differential equation \[ y^{\prime}+3 x^{2} y=12 x^{2} \] \[ \begin{array}{l} y=4+C e^{-x^{3}}, C \in \mathbb{R} \\ y=4-C e^{-x^{2}}, C \in \mathbb{R} \\ y=1+C e^{-x^{2 answers -
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Integrate. \[ \int 5 x^{2} \sin (8 x) d x=5\left(-\frac{1}{8} x^{2} \cos (8 x)+\frac{1}{256}(8 x \sin (8 x)+\cos (8 x))\right)+C \]2 answers -
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A B C D E F 1. \( \langle(\cos u+2) \cos v,(\cos u+2) \sin v, \sin u\rangle \) 2. \( \langle u \cos v, u, u \sin v\rangle \) 3. \( \left\langle 3 \cos ^{3} u \cos ^{3} v, 3 \sin ^{3} u \cos ^{3} v, 30 answers -
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\[ \text { "S" }=\left\{(x, y, z):(3 x)^{2}+z^{2}=y^{2}, 0 \leqslant y \leqslant 4\right\} \] Using stoke' Theorem verify \( F(x, y, z)= \) \[ -y i+2 x j+o k \]2 answers -
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d2x dt2 + 4x = −5 sen 2t + 9 cos 2t, x(0) = −1, x'(0) = 1 Resuelve el problema de valor inicial dado0 answers
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Trabaje con 3 decimales
Utilice el Teorema de Green para evaluar la integral de línea \( \int_{C}\left\langle 3 x y, 4 x^{2}-3 y\right\rangle \cdot d \mathbf{r} \), donde \( C \) es la recta de \( (0,3) \) a \( (3,9) \) y l2 answers -
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Pregunta 5 20 pts Use coordenadas polares para determinar el volumen del sólido dado. Bajo el plano \( 2 x+y+z=4 \) y sobre el disco \( x^{2}+y^{2} \leq 1 \) \( 9 \pi \) \( 4 \pi \) \( 3 \pi \) \( 52 answers -
Pregunta 4 \( 10 \mathrm{pts} \) Halle el volumen del sólido dado. Encerrado por el paraboloide \( z=x^{2}+y^{2}+1 \) y los planos \( x=0, y=0, z=0 \) y \( x+y=2 \) \begin{tabular}{l} \( 21 / 20 \) \2 answers -
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3. Use the Laplace transform to solve the initial value problems: a. \[ y^{\prime}+y=e^{-3 t} \cos 2 t, y(0)=0 \] b. \[ y^{\prime \prime}+4 y=10 \cos 5 t, y(0)=0, y^{\prime}(0)=0 \]2 answers -
4. Solve the initial value problem: \[ y^{\prime \prime}+4 y^{\prime}+4 y=(3+x) e^{-2 x}, \quad y(0)=2, y^{\prime}(0)=5 \]2 answers -
Una función \( w=f(x, y, z) \) es armónica si satisface la ecuación \[ \frac{\partial^{2} w}{\partial x^{2}}+\frac{\partial^{2} w}{\partial y^{2}}+\frac{\partial^{2} w}{\partial z^{2}}=0 \] Verifiq2 answers -
1. Integre la funcion sobre la region dada Triángulo \( f(x, y)=x^{2}+y^{2} \) sobre la región triangular con vértices \( (0,0),(1,0) \) y \( (0,1) \) 2. Use coordenadas cilíndricas Evalúe \( \ii2 answers -
Pregunta 2 20 pts Halle la masa de la lámina que ocupa la región \( D \) y que tiene la función de densidad \( \rho \) dada. D está acotada por \( y=1-x^{2} \) y \( y=x^{2} ; \rho(x, y)=k x^{2} \)2 answers -
solo necwsito el procedimiento porfa, ya esta la respuesta
Pregunta 6 \[ \int_{0}^{1} \int_{0}^{1} \int_{0}^{\sqrt{1-z^{2}}} \frac{z}{y+1} d x d z d y \] \[ \begin{array}{c} \frac{\ln 4}{3} \\ \frac{\ln 7}{3} \\ 5 \frac{\ln 2}{3} \\ \frac{\ln 2}{3} \end{array2 answers -
ya esta la respuesta, solo necesito procedimiento
Pregunta 7 \( 10 \mathrm{pts} \) \[ \int_{1}^{2} \int_{0}^{2 z} \int_{0}^{\ln x} x e^{-y} d y d x d z \] \begin{tabular}{c} \hline \( 15 / 18 \) \\ \hline \( 3 / 12 \) \\ \hline \( 5 / 3 \) \\ \hline2 answers -
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Given \( f(x, y)=-2 x^{6}-6 x^{2} y^{5}-4 y^{4} \) \[ f_{x}(x, y)= \] \[ f_{y}(x, y)= \] \[ f_{x x}(x, y)= \] \[ f_{x y}(x, y)= \]2 answers -
Pregunta 2 20 pts Halle la masa de la lámina que ocupa la región y que tiene la función de densidad \( \rho \) dada. D está acotada por \( y=1-x^{2} y \) \( y=x^{2} ; \rho(x, y)=k x^{2} \) \( \beg2 answers -
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Find \( y^{\prime \prime} \) \[ y=\frac{3 x+2}{2 x-1} \] \[ y^{\prime \prime}=\frac{28}{(2 x-1)^{3}} \]2 answers -
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1. \( \langle u \cos v, u \sin v, \pi \sin u\rangle \) 2. \( \langle\pi \sin v, \pi \cos u \sin 2 v, \pi \sin u \sin 2 v\rangle \) 3. \( \langle(1-|u|) \cos v,(1-|u|) \sin v, u\rangle \) 4. \( \langle0 answers -
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