Calculus Archive: Questions from November 19, 2022
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Find the absolute maxima and minima of \( f(x, y) \) on the given regions (1) \( f(x, y)=x^{2}+y^{2} \) on \[ R=\{(x, y) \mid 0 \leq x \leq 1, \quad 0 \leq y \leq 2-2 x\} \] (2) \( f(x, y)=x+x^{2}+2 y2 answers -
Given \( f(x, y)=6 x^{2}+4 x^{2} y^{6}+2 y^{4} \) \[ f_{x}(x, y)= \] \[ f_{y}(x, y)= \] \[ f_{x x}(x, y)= \] \[ f_{x y}(x, y)= \]2 answers -
35 ,38,42 please
Sketch the graph of each equation given in Problems 33-44. 33. \( y=\log x \) 34. \( y=\ln x \) 35. \( y-3=\ln x \) 36. \( y=\log x+4 \) 37. \( y=\log |x| \) 38. \( y=|\log x| \) 39. \( y=\log _{3} x2 answers -
Solve the initial value problem \[ \mathbf{y}^{\prime}=\left[\begin{array}{ccc} -1 & 4 & 2 \\ -2 & 5 & 2 \\ 1 & -2 & 0 \end{array}\right] \mathbf{y}, \quad \mathbf{y}(0)=\left[\begin{array}{c} 7 \\ 52 answers -
Establish the stability of equilibrium points of non-linear systems: In case there are no equilibrium points, modify some parameter until equilibrium points are found. This would be akin to redesignin
2. Establesca la estabilidad de puntos de equilibrio de los sistemas no-lineales: a) \( \frac{d y_{1}}{d t}=2 y_{1}-3 y_{2} \) \[ \frac{d y_{2}}{d t}=2 y_{1}^{2}+4 y_{1}-3 y_{2}+4 \] b) \( \frac{d y_{2 answers -
Find all the second partial derivatives. \[ \begin{array}{l} f(x, y)=x^{8} y^{7}+3 x^{6} y \\ f_{x x}(x, y)= \\ f_{x y}(x, y)= \\ f_{y x}(x, y)= \\ f_{y y}(x, y)= \end{array} \]2 answers -
\( f(x, y)=\left\{\begin{array}{ll}\frac{x y}{x^{2}+x y+y^{2}} & \text { if }(x, y) \neq(0,0) \\ 0 & \text { if }(x, y)=(0,0)\end{array}\right. \)0 answers -
0 answers
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Resuelva: 1. Halle \( r(t) \) para la siguiente condición \( r^{\prime}(t)=4 e^{2 t} i+3 e^{t} j, r(0)=2 i \) 2. Halle \( r^{\prime \prime}(t) \) de la siguiente función \( r(t)=4 \cos t i+4 \sin t2 answers -
2 answers
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2 answers
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Considere la siguiente gráfica para hallar los limites en de su función según solicitado. 1) \( \lim _{x \rightarrow-2-} f(x)= \) 2) \( \lim _{x \rightarrow-2} f(x)= \) 3) \( \lim _{x \rightarrow 02 answers -
Find the first partial derivatives of the function. \[ f(x, y, z)=\frac{6 x}{y+z} \] \[ f_{x}(x, y, z)= \] \[ f_{y}(x, y, z)= \] \[ f_{z}(x, y, z)= \]2 answers -
2 answers
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Find all the second partial derivatives. \[ f(x, y)=x^{7} y^{4}+3 x^{9} y \] \[ f_{x x}(x, y)= \] \[ f_{x y}(x, y)= \] \[ f_{y x}(x, y)= \] \[ f_{y y}(x, y) \bar{\tau} \] Additional Materials2 answers -
Una función \( y(t) \) satisface la ecuación diferencial \( \frac{d y}{d t}=y^{4}-6 y^{3}+5 y^{2} \). a. ¿Cuáles son las soluciones de equilibrio de la ecuación? b. ¿Para qué valores de \( y \)2 answers -
Find \( y^{\prime} \) and \( y^{\prime \prime} \). \[ y=e^{\alpha x} \sin (\beta x) \] \[ y^{\prime}= \] \[ y^{\prime \prime}= \]2 answers -
Halle todos los valores de equilibrio y utilice el Criterio de Estabilidad Local para determinar si cada equilibrio es localmente estable o inestable. \[ \frac{d p}{d t}=2 p(1-p)-p \]2 answers -
\( \int_{-3}^{3} \int_{0}^{\sqrt{9-x^{2}}} \operatorname{Sin}\left(x^{2}+y^{2}\right) d y d x \) Convert to polar: \( (r, \theta) \)2 answers -
(40 points) Solve the initial value problem \[ y^{\prime \prime}+4 x y^{\prime}-16 y=0, y(0)=8, y^{\prime}(0)=0 \text {. } \] \( y \)2 answers -
Find all the second partial derivatives. \[ f(x, y)=x^{9} y^{9}+6 x^{6} y \] \[ f_{x x}(x, y)= \] \[ f_{x y}(x, y)= \] \[ f_{y x}(x, y)= \]2 answers -
Find \( \mathrm{y}^{\prime \prime} \) \[ y=\left(x^{6}-x\right)^{5 / 6} \] Choose the correct expression for \( y^{\prime \prime} \) below. A. \( -\frac{5}{36}\left(x^{6}-x\right)^{-7 / 6}\left(6 x^{52 answers -
Considere la siguiente gráfica para hallar los limites en de su función según solicitado. 1) \( \lim _{x \rightarrow 2_{-7}} f(x)= \) 2) \( \lim _{x \rightarrow-2^{+}} f(x)= \) 3) \( \lim _{x \righ2 answers -
Halle todos los valores de equilibrio de la ecuación diferencial autónoma dada. \[ \frac{d y}{d t}=y(3-y)\left(25-y^{2}\right) \]2 answers -
Halle la solución de la ecuación diferencial que satisface la condición inicial dadz \[ 2 x y^{\prime}-\ln \left(x^{2}\right)=0, \quad y(1)=2 \]2 answers -
Halle la solución de la ecuación diferencial que satisface la condición inicial dada. \[ \frac{d u}{d t}=\frac{2 t+\sec ^{2} t}{2 u}, u(0)=-5 \]2 answers -
Use \( f(x, y, z)=x^{2}+y z, \vec{F}(x, y, z)=\langle x y, y z, x z\rangle \), and \( \vec{G}(x, y, z)=\left\langle-\sin (z), e^{x z}, y\right\rangle \). Compute \( (\vec{F} \times \vec{G})(9,-1,3) \)2 answers -
2 answers
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Solve the integral: Where:
\( \iint_{\Psi} \mathbf{F} \cdot d \mathbf{S} \) \( \Psi(\theta, \phi)=(7 \cos \theta \sin \phi, 7 \sin \theta \sin \phi, 7 \cos \phi), \quad 0 \leq \theta \leq 2 \pi, 0 \leq \phi \leq \pi \) \( \ma2 answers -
thanks
3. La curva cerrada \( \Gamma \) consiste de 4 segmentos recorridos en sentido positivo con vértices en \( (1,2),(3,2)),(3,5),(1,5) \) Calcule \[ \int_{\Gamma} x^{2} d x+\left(y e^{-y^{2}}+x^{2}\righ2 answers -
2 answers
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Find all the second partial derivatives. \[ \begin{array}{l} f(x, y)=x^{8} y^{7}+5 x^{5} y \\ f_{x x}(x, y)=\mid \begin{array}{l} f_{x y} \end{array} \\ f_{y x}(x, y)=56 x^{7} y^{6}+25 x^{4} \\ f_{y x2 answers -
Find all the second partial derivatives. \[ \begin{array}{l} f(x, y)=x^{8} y^{7}+5 x^{5} y \\ f_{x x}(x, y)=\mid \begin{array}{l} f_{x y} \end{array} \\ f_{y x}(x, y)=56 x^{7} y^{6}+25 x^{4} \\ f_{y x2 answers -
2 answers
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2 answers
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ts) Calculate the Laplacian of \( f(x, y)=x^{7} y^{8}+2 x \sin (3 y) \) : \[ \Delta f(x, y)=\nabla^{2} f(x, y)=\frac{\partial^{2} f(x, y)}{\partial x^{2}}+\frac{\partial^{2} f(x, y)}{\partial y^{2}} \2 answers -
2 answers
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\[ \mathbf{F}(x, y, z)=\left(7 x^{6} \ln \left(6 y^{2}+2\right)+9 z^{3}\right) \mathbf{i}^{\mathbf{4}}+\left(\frac{12 y x^{7}}{6 y^{2}+2}+2 z\right) \mathbf{j}+\left(27 x z^{2}+2 y-2 \pi \sin \pi z\ri2 answers -
Q1 F'x G'x
(1 point) Shown below is the graph of \( y=f^{\prime}(x) \), NOT the graph of \( y=f(x) \). (Click on picture for a better view.) Then from this information, we can conclude that the best approximatio2 answers -
2 answers
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1. Solve the initial value problem \[ \mathbf{y}^{\prime}=\left[\begin{array}{ccc} -1 & 4 & 2 \\ -2 & 5 & 2 \\ 1 & -2 & 0 \end{array}\right] \mathbf{y}, \quad \mathbf{y}(0)=\left[\begin{array}{c} 7 \\2 answers