Calculus Archive: Questions from November 02, 2023
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Seleccionar la opción que contiene el valor de y(0.1), calculado mediante el método de Runge Kutta de cuarto orden con \( \mathrm{h}=0.1 \) para la ecuación \( \quad y \prime=y-x \quad y(0)=2 \) a)1 answer -
Seleccionar la opción que contiene el valor de \( \mathrm{y}(1) \), calculado mediante el método de Euler con \( \mathrm{h}=0.25 \) para la ecuación \( y \prime=y-x \) \( y(0)=2 \) a) 4.567 b) 4.491 answer -
Seleccionar la opción que contiene la forma correcta de la solución particular por el método de los coeficientes indeterminados de la ecuación: \( y^{\prime \prime}-y^{\prime}-2 y=10 \operatorname1 answer -
Seleccionar la opción que contiene la naturaleza del punto de equilibrio del sistema \( x^{\prime}=x-3 y \ldots \ldots y^{\prime}=-2 x+y \) a) Atractor b) Repulsor c) Punto Silla C b a1 answer -
Dos tanques cada uno con \( 50 \mathrm{~L} \) de líquido, están interconectados por tubos con líquido fluyendo del tanque \( \mathrm{A} \) al tanque \( \mathrm{B} \) a razón de \( 4 \mathrm{~L} /1 answer -
Find fx(x, y) and fy(x, y) given that
(e) \( f(x, y)=x \sqrt{y} \) (f) \( f(x, y)=2 y^{2} \sqrt{x} \) (g) \( f(x, y)=x^{2}-4 x y+3 y^{2} \) (h) \( f(x, y)=\frac{x y}{x^{2}+y^{2}} \)1 answer -
Find y' if tan^-1(x^2y)=x+xy^2
Find \( y^{\prime} \), if \( \tan ^{-1}\left(x^{2} y\right)=x+x y^{2} \)1 answer -
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i If y = sin-¹ (5x), then 1 (A) 1+25x² (B) (C) (D) (E) 5 1+25x² √1-25x² 1 √1-25x² 5 √1-25x² =
If \( y=\sin ^{-1}(5 x) \), then \( \frac{d y}{d x}= \) (A) \( \frac{1}{1+25 x^{2}} \) (B) \( \frac{5}{1+25 x^{2}} \) (C) \( \frac{-5}{\sqrt{1-25 x^{2}}} \) (D) \( \frac{1}{\sqrt{1-25 x^{2}}} \) (E) \1 answer -
If y = arctan(cos x), then dy - sin æ 1+cos³I = (A) (B) -(arcsec(cos x))² sin x (C) (arcsec(cos x))² 1 (D) (arccos x)² +1 1 (E) 1+ cos²x
If \( y=\arctan (\cos x) \), then \( \frac{d y}{d x}= \) (A) \( \frac{-\sin x}{1+\cos ^{2} x} \) (B) \( -(\operatorname{arcsec}(\cos x))^{2} \sin x \) (C) \( (\operatorname{arcsec}(\cos x))^{2} \) (D)1 answer -
Evaluate sin²(0) r. dr dº.
Evaluate \( \int_{0}^{\pi} \int_{0}^{2} \sin ^{2}(\theta) r \mathrm{~d} r \mathrm{~d} \theta \)1 answer -
Solve each of the following differential equations. (b) \( \frac{d y}{d x}-y=e^{x}(1+\ln x) \) (f) \( \left(1+\frac{1}{x}\right) \tan y+\left(\sec ^{2} y\right) \frac{d y}{d x}=0 \)1 answer -
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Differentiate the function. \[ \begin{array}{l} y=\ln \left(\left|6+t-t^{3}\right|\right) \\ y^{\prime}= \end{array} \]1 answer -
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Find the general solution of:
\( y^{V}-y^{I V}-2 y^{\prime \prime \prime}+2 y^{\prime \prime}+y^{\prime}-y=0 \)1 answer -
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Find all the complex roots. Leave your answers in polar form with the argument in degrees. The complex fourth roots of -16 \[ \begin{array}{l} \sqrt[4]{2}\left(\cos 45^{\circ}+i \sin 45^{\circ}\right)1 answer -
Just do Number 59 Please.
57-62. Changing order of integration Reverse the order of integration in the following integrals. 57. \( \int_{0}^{2} \int_{x^{2}}^{2 x} f(x, y) d y d x \) 58. \( \int_{0}^{3} \int_{0}^{6-2 x} f(x, y)1 answer -
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14. Calcule la integral \[ \int_{C}(x+y)^{2} d x-\left(x^{2}+y^{2}\right) d y \] donde \( C \) es el triángulo con vértices en los puntos \( (0,0),(1,0),(0,1) \) recorrido en sentido antihorario.1 answer -
Let f(x, y) = sin2(x) cos(y). Calculate 22 дхду f.
Let \( f(x, y)=\sin ^{2}(x) \cos (y) \). Calculate \( \frac{\partial^{2}}{\partial x \partial y} f \).1 answer -
Implicit Differentiation Find \( \frac{d^{2} y}{d x^{2}} \) \[ x+9 y=5 \sin (y) \] \[ \frac{d^{2} y}{d x^{2}}= \]1 answer -
Find all the second partial derivatives. \[ \begin{array}{l} \quad f(x, y)=\ln (a x+b y) \\ f_{x x}(x, y)= \\ f_{x y}(x, y)= \\ f_{y x}(x, y)= \\ f_{y y}(x, y)= \end{array} \]1 answer -
Given \( f(x, y, z)=\sqrt{2 x+3 y+5 z} \) \[ f_{x}(x, y, z)= \] \[ f_{y}(x, y, z)= \] \[ f_{z}(x, y, z)= \]1 answer -
Given \( f(x, y)=6 e^{3 x} \sin (2 y) \) \[ \nabla f(0, \pi)= \] Given \( f(x, y)=6 e^{3 x} \sin (2 y) \) \[ \nabla f(0, \pi)= \]1 answer -
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