Calculus Archive: Questions from June 13, 2023
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5- If \( w=x^{2}+y-z+\cos t \) and \( x+y=t \), then the value of \( \left(\frac{\partial w}{\partial x}\right)_{y, z} \) is equal to \( 2 x+\cos (x+y) \) b) \( \quad x y-\cos (x+y) \) c) \( 2 x-\sin2 answers -
5- If \( w=x^{2}+y-z+\cos t \) and \( x+y=t \), then the value of \( \left(\frac{\partial w}{\partial x}\right)_{y, z} \) is equal to a) \( 2 x+\cos (x+y) \) b) \( x y-\cos (x+y) \) c) \( 2 x-\sin (x+2 answers -
Google Classroom Encuentra los valores de x. Ingresa las soluciones de menor a mayor. x^(2)+12x+27=02 answers
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f(x) (x, y) = (x, y) = x² x-1 0,0 1.2 X
\( \begin{array}{c}f(x)=\frac{x^{2}}{x-1} \\ (x, y)=0,0\end{array} \)0 answers -
For given function \( f(x, y)=\sin \left(y+e^{x}\right) \), match the derivatives \( f_{x}, f_{y}, f_{x y}, f_{x x} \) with the correct functions given below. A. \( e^{x} \cos \left(e^{x}+y\right) \)2 answers -
\( y^{\prime \prime \prime}+y^{\prime \prime}=\cos (2 x), \quad y(0)=1, y^{\prime}(0)=2, y^{\prime \prime}(0)=3 \)2 answers -
2. \( y^{\prime \prime \prime}+y^{\prime \prime}=\cos (2 x), \quad y(0)=1, y^{\prime}(0)=2, y^{\prime \prime}(0)=3 \)2 answers -
Solve the following differential equation by the separable variable method. What is your general solution?
Resuelva la siguiente ecuación diferencial por el método de variable separable. ¿Cuál es su solución general? \[ \begin{array}{r} y^{\prime}=\frac{x^{2} y-y}{y+1} \\ y+\ln y=\frac{x^{3}}{3}+c \\2 answers -
We have that y = ce-X + cze-3x - 1 15 sin (3x) - TCOS(3x) is the general solution of the equation y" + 4y + 3y = 2sin (3x) What are the values of C and C, obtained by determining a particular so
una solución particular que cumpla las condiciones iniciales \[ y(0)=5 \text { y } y^{\prime}(0)=4 \text { ? } \] \[ c_{1}=\frac{49}{5} y c_{2}=\frac{-14}{3} \] \[ c_{1}=\frac{14}{9} \text { y } c_{22 answers -
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Encuentre el área de la superficie obtenida al rotar la curva. y = x 2 , 0 ≤ x ≤ 1, sobre el eje y .2 answers
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10 dx/(4+4x^2)^2 x = tan(theta)
10. \( \int_{0}^{1} \frac{d x}{\left(4+4 x^{2}\right)^{2}}, \quad x=\tan \theta \)2 answers -
Given \( f(x, y)=6 x^{2}+x y^{4}-3 y^{5} \) \[ \begin{array}{l} f_{x x}(x, y)=[ \\ f_{x y}(x, y)=[ \end{array} \]2 answers -
\( y=\sin (x), \quad y=0, \quad 0 \leq x \leq \pi ; \) about \( y=-3 \) \( \int^{\pi}\left(x^{\pi}\right) d x \)0 answers -
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Obtenga la ecuación del conjunto de todos los puntos equidistantes de los puntos \( A(-1,5,3) \) y \( B(6,2,-2) \). Describa el conjunto.2 answers -
Equilibrio de tensiones Una pesa de \( 100 \mathrm{lb} \) pende de una cuerda, como se muestra en la figura siguiente. Encuentre las tensiones \( \mathbf{T}_{1} \) y \( \mathbf{T}_{2} \) en la cuerda.2 answers -
Si \( \mathbf{a} \cdot \mathbf{b}=\sqrt{3} \) y \( \mathbf{a} \times \mathbf{b}=\langle 1,2,2\rangle \), encuentre el ángulo entre a y b.2 answers -
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Select the correct answer. A linear differential equantion is given by: (e is none of the above).
Una ecuación diferencial lineal está dada por: a. \( \quad x \frac{d^{3} y}{d x^{3}}-\left(\frac{d^{4} y}{d x^{4}}\right)^{4}+y=0 \) b. \( \frac{d^{2} u}{d r^{2}}+\frac{d u}{d r}+u=\cos (r+u) \) c.2 answers -
Select the correct answer. The values of m for which the function y=e^(mx) is a solution to the differential equation y''-5y'+6y=0 are: (d means infinite solutions, and e means none of the above).
Los valores de \( m \) para los cuales la función \( y=e^{m x} \) es solución de la ecuación diferencial \( y^{\prime \prime}-5 y^{\prime}+6 y=0 \) son: a. \( m_{1}=-2, m_{2}=-3 \) b. \( m_{1}=2, m2 answers -
Select the correct answer. The points of equilibrium of the differential equation dy/dx = yln(y+2) are: (d means infinite critical points, and e means has no points of equilibrium).
Los puntos de equilibrio de la ecuación diferencial \( \frac{d y}{d x}=y \ln (y+2) \) son: a. \( y_{1}^{*}=0, y_{2}^{*}=1 \) b. \( y_{1}^{*}=0, y_{2}^{*}=-1 \) c. \( y_{1}^{*}=0, y_{2}^{*}=-2 \) d. c2 answers -
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Equilibrio de tensiones Una pesa de \( 100 \mathrm{lb} \) pende de una cuerda, como se muestra en la figura siguiente. Encuentre las tensiones \( \mathbf{T}_{1} \) y \( \mathbf{T}_{2} \) en la cuerda.2 answers