Calculus Archive: Questions from September 17, 2022
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I NEED TO HAVE ANSWER ASAP
Integrable Combinations \( (\mathrm{ydx}-\mathrm{x} d y)\left(\mathrm{x}^{3}+2 \mathrm{xy}^{2}+\mathrm{x}^{2} \mathrm{y}+\mathrm{y}^{3}\right)=0 \) \( -\left(y^{2}+x^{2} y \sin x\right) d x+\left(x y+2 answers -
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Demonstrate whether the following series are convergent or divergent
Demuestre si las siguientes series son convergentes o divergentes 1. \( 1+\frac{1}{8}+\frac{1}{27}+\frac{1}{64}+\frac{1}{125}+\cdots \) 2. \( \frac{1}{5}+\frac{1}{8}+\frac{1}{11}+\frac{1}{14}+\frac{1}2 answers -
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Determinar cuando la serie es absolutamente convergente, condicionalmente convergente o divergente. 1. \( \sum_{n=1}^{\infty} \frac{(-1)^{n+1}}{2 n^{2}} \) 2. \( \sum_{n=1}^{\infty} \frac{(-1)^{n}}{\s1 answer -
II. Evalúe los integrales. a) \( \int\left(9 x^{3}-x\right)^{2} d x \) b) \( \int \sec (x)\left(\frac{\operatorname{sen}(x)-1}{\cos (x)}\right) d x \) c) \( \int \frac{1}{(3 x)^{2}} d x \)1 answer -
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True or False
La gráfica de la curva solución de la ecuación diferencial \( y^{\prime}=x \) que satisface \( y(0)=0 \) es1 answer -
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Find the gradient of the functions a) \[ f(x, y)=\ln \left(e^{x}+e^{y}\right) \] b) \[ f(x, y)=\frac{x y}{x-y} \] c) \[ f(x, y, z)=(5 x+7 y+11 z)^{15} \]1 answer -
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Find which of the following functions is harmonic. a) b) \[ f(x, y)=3 x^{2} y-y^{3} \] c) \[ f(x, y)=\ln \sqrt{x^{2}+y^{2}} \] d) \[ f(x, y)=e^{-x} \sin y-e^{-y} \sin x \] \[ f(x, y)=e^{y} \cos x+e^{x1 answer -
Find the potential function \( f \) for the field \( F \). \[ \begin{aligned} F=&\left\{\frac{-x y z}{\left(1+x^{2}\right)^{3 / 2}}, \frac{z}{\left(1+x^{2}\right)^{1 / 2}}, \frac{y}{\left(1+x^{2}\righ1 answer -
Find the potential function \( f \) for the field \( F \). \[ \begin{aligned} \mathbf{F}=& \frac{x}{z^{2} \sqrt{x^{2}+y^{2}}} \mathbf{i}+\frac{y}{z^{2} \sqrt{x^{2}+y^{2}}} \mathbf{j} \cdot \frac{2 \sq1 answer -
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classify ODEs: (1) \( y^{\prime \prime}+2 y^{\prime}+e^{y}=x \) (2) \( 3 x^{2} y^{\prime \prime}+2 \ln (x) y^{\prime}+e^{x} y=3 x \cos x \) (3) \( 4 y y^{\prime \prime}-x^{3} y^{\prime}+\cos y=e^{2 x}2 answers -
Derivative Practice
\( \begin{array}{ll}\mathrm{h}(\mathrm{x})=\frac{1+\sqrt[3]{x}}{\cos x} & \text { (f) } \mathrm{N}(\mathrm{t})=\frac{3 x-1}{1+x^{2}} \\ \mathrm{y}=\cos \mathrm{x} \tan \mathrm{x} & \text { (h) } \math1 answer -
Evaluate the integral. \[ \begin{array}{c} \int\left(\cos (2 \pi t) \mathbf{i}+\sin (5 \pi t) \mathbf{j}+t^{3} \mathbf{k}\right) d t \\ \sin \left(\frac{2 \pi t}{2 \pi}+c_{1}\right) \mathbf{i}+\left(\1 answer -
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La solución de la ED \( \left(x y^{2}+4 x\right) d x+\left(x^{2} y+y\right) d y=0, y(1)=2 \), es: a. \( \left(1+x^{2}\right)\left(4+y^{2}\right)=4 \) b. \( \left(1+x^{2}\right)\left(4+y^{2}\right)=161 answer -
I. Aplique los procesos estudiados para resolver problemas de valor inicial para obtener la solución particular de acuerdo a las condiciones dadas por el ejercicio. a) Determine \( f(x) \) para \( f^1 answer -
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\( y=f(x) \quad y=g(x) \) Use the graphs of \( y=f(x) \) and \( y=g(x) \) above to the find the function value. (a) \( (g \circ f)(0)= \) (b) \( (g \circ g)(2)= \)1 answer -
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