Calculus Archive: Questions from November 09, 2023
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Solve Initial Value problem.(4) + 2 + 1 = 0, y(0) = 1, y(0) = 2, y"(0) = 3, y" (0) = 0.
\( y^{(4)}+2 y^{\prime \prime}+1 y=0, y(0)=1, y^{\prime}(0)=2, y^{\prime \prime}(0)=3, y^{\prime \prime \prime}(0)=0 \).1 answer -
Find the derivative of y=(2x−x^2)e^5x
Find the derivative of \( y=\left(2 x-x^{2}\right) e^{5 x} \) \[ \begin{array}{l} y^{\prime}=(2-2 x) e^{5 x}-\left(2 x-x^{2}\right) e^{5 x}(5) \\ y^{\prime}=5(2-2 x) e^{5 x} \\ y^{\prime}=(2-2 x) e^{51 answer -
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Actividad 8. Suma de funciones periódicas. Considere las funciones ƒ(t) = sen(t) y g(t) = sen( 2πt) y calcule sus respectivos periodos. Haga la gráfica de f(t)+ g(t) y observe que no es periódica
Actividad 8. Suma de funciones periódicas. Considere las funciones \( f(t)=\operatorname{sen}(t) \) y \( g(t)=\operatorname{sen}(2 \pi t) \) y calcule sus respectivos periodos. Haga la gráfica de \(1 answer -
For F(x, y, z) = 3xyz² + y² sin z3 + xe²k find (a) div F (b) curl F
For \( \vec{F}(x, y, z)=3 x y z^{2} \hat{i}+y^{2} \sin z \hat{j}+x e^{2 z} \hat{k} \) find (a) \( \operatorname{div} \vec{F} \) (b) curl \( \vec{F} \)1 answer -
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Let \( f(x)=3 \tan ^{-1}\left(3 e^{x}\right) \) \[ f^{\prime}(x)=-\frac{9 e^{x}}{\sin \left(3 e^{x}\right)^{2}} \]1 answer -
\( \begin{array}{l}g(x, y)=f(x-2, y) \\ g(x, y)=f(x, y+2) \\ g(x, y)=f(x+3, y-4)\end{array} \) Describe how the graph of \( g \) is obtained from the graph of \( f \) \[ \begin{array}{l} g(x, y)=f(x,1 answer -
Describe the domain and range of the function. \[ f(x, y)=\sqrt{64-x^{2}-y^{2}} \] Domain: \( \left\{(x, y): x^{2}+y^{2} \leq 64\right\} \) \( \left\{(x, y): x^{2}+y^{2}1 answer -
3. \( y=e^{\cos (x)}+\tan \left(e^{3 x}\right) \) \( -e^{\cos (x)} \sin (x)+\frac{3 e^{3}}{\cos ^{2}} \) \[ \begin{array}{l} h(x)=2 \tan \left(x^{3}\right)+\ln \left(5 x^{2}+2\right) \\ 6 x^{2} \sec ^1 answer -
ifferentiate the functions: \[ \begin{array}{l} y=\ln \sqrt{\frac{x^{3} \tan x}{\left(3 x^{2}+7\right)}} \\ y=\left(5 x^{2}+2 x\right)^{\ln x} \\ h(x)=x^{3} \cot x \arccos 3 x \end{array} \]1 answer -
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Let y = dy dx 7x-² + 6x-¹-5. Find y if y(1) = 4.
Let \( \frac{d y}{d x}=7 x^{-2}+6 x^{-1}-5 \). Find \( y \) if \( y(1)=4 \). \[ y= \]1 answer -
\[ \sum_{k=0}^{\infty}(-1)^{k}\left(\frac{k \cdot(x-3)^{k}}{5^{k}}\right) \] Radius \( = \) , Interval: \[ \sum_{k=0}^{\infty} \frac{x^{2 k+1}}{4^{k-1}} \] Radius \( = \) , Interval:1 answer -
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Solve the IVP \( y^{\prime \prime}-2 y^{\prime}+y=g(t) \), where \( y(0)=0, y^{\prime}(0)=1 \), and \[ g(t)=\left\{\begin{array}{ll} 0, & t2 answers -
formulas) Formulas) x' = = y y = 12x + 4y x(0) = 0 y(0) = 1
\( \begin{array}{ll}x^{\prime}=y & x(0)=0 \\ y^{\prime}=12 x+4 y & y(0)=1\end{array} \) Solve \[ \begin{array}{ll} x^{\prime}=y & x(0)=0 \\ y^{\prime}=12 x+4 y & y(0)=1 \end{array} \] \( x(t)=-\frac{1 answer -
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Solve \[ \begin{array}{ll} x^{\prime}=y-x+t & x(0)=2 \\ y^{\prime}=y & y(0)=6 \end{array} \] \[ x(t)= \] help (formulas) \[ y(t)= \] help (formulas)1 answer -
1. Determine the following integrals: (i) \( \int 40 x\left(20 x^{2}-30\right)^{3} d x \) (ii) \( \int 6 x\left(9 x^{2}-20\right)^{4} d x \)1 answer -
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1) Let y = 4x-2 x²+x 5
Let \( y=\left(\frac{4 x-2}{x^{2}+x}\right)^{5} \) 1) Let \( y=\left(\frac{4 x-2}{x^{2}+x}\right)^{5} \), Find \( y^{\prime} \cdot\left(\frac{5(4 x-2)^{4}\left(-4 x^{2}+4 x+2\right)}{\left(x^{2}+x\ri1 answer -
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Determine the signs of the partial derivatives of the function f whose graph is illustrated.
Determine los signos de las derivadas parciales de la función f cuya gráfica se ilustra. Signo de \( f_{x}(1,2) \) A. 0 Signo de \( f_{y}(1,2) \) B. Negativo c. Positivo0 answers -
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y' = −2e¹ - 6x³ + 4x +3 y(0) = 7
\( \begin{array}{c}y^{\prime}=-2 e^{x}-6 x^{3}+4 x+3 \\ y(0)=7\end{array} \)1 answer -
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Resolver utilizando cálculo vectorial Conseguir las dos derivadas parciales de primer orden del ejercicio 5 al 28
En los ejercicios 5 a 28 , hallar las dos derivadas parciales de primer orden. 5. \( f(x, y)=2 x-3 y+5 \) 6. \( f(x, y)=x^{2}-3 y^{2}+7 \) 7. \( z=x \sqrt{y} \) 8. \( z=2 y^{2} \sqrt{x} \) 9. \( z=x^{1 answer -
i am having problem with #32 please help me and please explain it as much as possible thanks
19-36 Sketch the region enclosed by the given curves and find its area. 19. \( y=12-x^{2}, \quad y=x^{2}-6 \) 20. \( y=x^{2}, \quad y=4 x-x^{2} \) 21. \( x=2 y^{2}, \quad x=4+y^{2} \) 22. \( y=\sqrt{x1 answer -
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3. Sea \( f(x)=\sqrt[3]{x} \). Escriba la formula \( y \) dibuje la gráfica de cada una de las siguientes utilizando las transformaciones: a. Estiramiento horizontal por un factor de 3, seguido de un1 answer -
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\( \begin{array}{l}y^{\prime}\left(\text { or } \frac{d y}{d x}\right) \text { if } x e^{25 y}-10 x^{4}+5 x y^{5}=10 \\ y^{\prime}=\frac{40 x^{3}+5 y^{5}+e^{25 y}}{25 x e^{25 y}+25 x y^{4}} \\ y^{\pri1 answer -
\( \begin{array}{l} y^{\prime} \text { (or } \frac{d y}{d x} \text { ) if } \ln (21 y) \sin x=x y^{8}+12 x^{5} \\ y^{\prime}=\frac{y^{9}-y \ln (21 y) \cos x+60 x^{4} y}{\sin x-8 x y^{8}} \\ y^{\prime}1 answer -
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3. 2 puntos Muestre cjemplos de una funciones \( f, g, h \). Funcioues escalares o vectoriales, segtin sea el a) Vficel pradiente de \( f \) b) \( \nabla \cdot g: \) es la divempencia de \( g \) c) \(1 answer -
\( \int \frac{d x}{\sqrt{-2 x+8 x+4}} \quad \int_{\pi / 8}^{\pi / 4}(\csc 2 \theta-\cot 2 \theta) d \theta \)1 answer -
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\( \begin{array}{l}y^{\prime}\left(\text { or } \frac{d y}{d x}\right) \text { if } x e^{3 y}-14 x^{4}+5 x y^{9}=7 \\ y^{\prime}=\frac{56 x^{3}+5 y^{9}+e^{3 y}}{3 x e^{3 y}+45 x y^{8}} \\ y^{\prime}=\1 answer -
\( \begin{array}{l}y^{\prime} \text { (or } \frac{d y}{d x} \text { ) if } \ln (22 y) \sin x=x y^{9}+12 x^{7} \\ y^{\prime}=\frac{y^{10}-y \ln (22 y) \cos x+84 x^{6} y}{\sin x-9 x y^{9}} \\ y^{\prime}1 answer -
Determina el valor promedio del campo escalar \( f(x, y, z)=x+y+z \) a lo largo de la curva paramentrizada por \[ \gamma(t)=(\sin (t), \cos (t), t), \] \( \operatorname{con} t \in[0,2 \pi] \). Detern1 answer -
Sea \( F(x, y)=(-y, x) \). Prueba que si \( \Gamma \) es una curva cerrada simple parametrizada en el sentido de las manecillas del reloj por \( \gamma \), y \( D \) es la región acotada por \( \Gamm1 answer -
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Describe the domain and range of the function. \[ f(x, y)=\sqrt{25-x^{2}-y^{2}} \] Domain: \[ \begin{array}{l} \left\{(x, y): x^{2}+y^{2} \geq 25\right\} \\ \left\{(x, y): x^{2}+y^{2} \leq 25\right\}1 answer -
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