Calculus Archive: Questions from October 20, 2022
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Describe the domain and range of the function. \[ f(x, y)=3 x^{2}-y \] Domain: \[ \begin{array}{l} \{(x, y): x \geq 0, y \geq 0\} \\ \{(x, y): x \text { is any real number, } y \text { is any real num2 answers -
17) \( \int \frac{225 x^{4}+50 \sqrt[3]{x^{2}}+42 \sqrt[5]{x^{2}}}{15} d x \) A) \( 3 x^{4}+2 x^{\frac{2}{3}}+2 x^{\frac{2}{5}}+C \) B) \( 15 x^{5}+\frac{10 x^{\frac{5}{3}}}{3}+\frac{14 x^{\frac{7}{5}2 answers -
Evaluate the integral using the Fundamental Theorem of the Line Integral a) smooth curve from (0,0) to (3,8) b) smooth curve from (0, -π) to (3π/2, π/2)
II: Evalúe el integral utilizando el Teorema fundamental del integral de línea a) \( \int_{c}(3 y i+3 x j) \cdot d r \) C: curva suave desde \( (0,0) \) hasta \( (3,8) \) b) \( \int_{c} \cos (x) \op2 answers -
Calculate, given that
6. Calcular \( \int_{\Gamma} \varphi d s \) dado que: a) \( \varphi(x, y, z)=e^{\sqrt{z}}, \Gamma(t)=\left(1,2, t^{2}\right), t \in[0,1] \) b) \( \varphi(x, y, z)=x+y+z, \Gamma(t)=(t, 2 t,-3 t), t \in2 answers -
5. Calculate the work done by the force field F(x,y,z)=(y,4x,2y), when moving a particle along the curve r(t)=(t^3,2t,t^ 2) from the origin to point A (8,4,4)
5. Calcular en trabajo realizado por el campo de fuerzas \( F(x, y, z)=(y, 4 x, 2 y) \), al mover una partícula a lo largo de la curva \( r(t)=\left(t^{3}, 2 t, t^{2}\right) \), desde el origen hasta2 answers -
Exercise 3 Please
3. Sean \( F: \mathbb{R}^{3} \rightarrow \mathbb{R}^{3}, G: \mathbb{R}^{3} \rightarrow \mathbb{R}^{3} \), dos campos vectoriales. Demostrar que: a) \( \operatorname{rot}(F+G)=\operatorname{rot} F+\ope2 answers -
Exercise 4 Please
a) \( \operatorname{rot}(F+G)=\operatorname{rot} F+\operatorname{rot} G \), b) \( \operatorname{div}(F+G)=\operatorname{div} F+\operatorname{div} G \) 4. Calcular de la forma más simple \( \int_{C} y2 answers -
Resolve Excercise 1 Please
1. The trajectory \( C \) is constituted by the line segment that goes from the point \( A(0,3) \) to \( B(3.9) \). followed by the arc of the parabola \( y=x^{2} \), from the point \( B(3,9) \) to th2 answers -
Resolve exercise 2 please
2. If \( F \) is the vector field defined by \( F(x, y, z)=\left(8 x y+4 z 2,4 x 2-8 y z, 8 x z-4 y^{2}\right) \) and \( C \) is the trace of the sphere \( E: x 2+y^{2}+z 2=16 \) with the \( x z \) pl2 answers -
8. Find the Partials: \( 10 \mathrm{pts} \) a) \( f_{x}(x, y) \) b) \( f_{y}(x, y) \) \[ f(x, y)=(x y-1)^{5} \]2 answers -
1. Encontrar la derivada de las siguientes expresiones. \( 5 \mathrm{pts} / \mathrm{cd} \) a. \( 10 \ln \sin ^{1} x \) c. \( \frac{d}{d x}\left(05^{-1}(2 x)\right. \) d. \( \frac{d}{d x}\left(\cos ^{-2 answers -
integrate the following expressions
2. Integrar las siguientes expresiones. \( 5 \mathrm{pts} / \mathrm{cd} \) i. Integración por partes a. \( \int x^{\prime \prime} \sin x^{4} d x \) b. \( \int x^{2} \sin 2 x d x \)1 answer -
28) If \( f(x)=\frac{8}{\sin x} \), then find \( \frac{d y}{d x} \) in terms of \( \csc \) and \( \cot \). 29) If \( y=\sqrt{2} \sec x \), than find \( y^{\prime} \) in terms of \( \sec \) and \( \tan2 answers -
integration for parts integrate the following expressions
Integración por partes a. \( \int x^{\prime \prime} \sin x^{4} d x \)2 answers -
Help and with FULL WORK!!!THANKS
\( y=x^{2} \sec x \) \( y=\frac{x^{3}-\cos x}{x^{3}+\sin x} \) \( y=\frac{(\csc x+\cot x)(\sin x)}{1+\cos x} \) Problem 1: Find the following derivatives: ( 2 points each) a) \( y=x^{2} \sec x \) b)2 answers -
please solve all the qusrions with steps
In exercises 1 눈-10또, find all first-order partial derivatives. 1. \( f(x, y)=x^{3}-4 x y^{2}+y^{4} \) - \( \{ \) A: 2. \( f(x, y)=x^{2} y^{3}-3 x \) 3. \( f(x, y)=x^{2} \sin x y-3 y^{3} \) - A⿺2 answers -
1 point) Let \( F=(x+y) \exp (x+y), x=\ln (u) \), and \( y=v \). Find \( \frac{\partial F}{\partial v} \). Your answer should be in terms of \( x, y, u \), and \( v \). A. \( \exp (x+y)+(x+y) \exp (x+2 answers -
La siguiente representa el volumen de un sólido: \[ \pi \int_{2}^{4} y^{4} d y \] Dibuje la gráfica utilizando un graficador en linea y describa el sólido. Puede utilizar el siguiente enlace: http:0 answers -
13. \( f(x, y)=\ln \left(x^{4}\right)-3 x^{2} y^{3}+5 x \underline{t a n}^{-1} y ; f_{x x}, f_{x y}, f_{x y y}- \) A 14. \( f(x, y)=e^{4 x}-\sin \left(x+y^{2}\right)-\sqrt{x y} ; f_{x x}, f_{x y}, f_{2 answers -
\( y=\ln (4+\ln (x)) \) \( y^{\prime}=\frac{1}{x \ln (x)+4} x \) \( y^{\prime \prime}=\frac{5+\ln (x)}{x^{2}(\ln (x)+4)^{2}} \)2 answers -
\[ y=\ln \left(1-2 x-x^{2}\right) \] relative minimum \( (x, y)=(-1-\sqrt{2}) \) relative maximum \( (x, y)= \)2 answers -
\( y^{\prime}=\frac{x}{\left(e^{\left.x^{2}\left(x^{2} \ln \left(25 x^{8}\right)\right)+4\right)} \ln \left(5 x^{4}\right)\right.} \)2 answers -
point) Let \( F=(x+2 y) \exp (x+y), x=u \), and \( y=\ln (v) \). Find \( \frac{\partial F}{\partial v} \). Your answer should be in terms of \( x, y, u \), an A. \( \frac{2 \exp (x+y)+(x+2 y) \exp (x+2 answers -
1 point) Let F=(4x+y)exp(x+y),x=ln(u), and y=v.F=(4x+y)exp(x+y),x=ln(u), and y=v. Find ∂F∂v∂F∂v. Your answer should be in terms of xx, yy, uu, and vv.
point) Let \( F=(4 x+y) \exp (x+y), x=\ln (u) \), and \( y=v \). Find \( \frac{\partial F}{\partial v} \). Your answer should be in terms of \( x, y, u \), and A. \( (4 \exp (x+y)+(4 x+y) \exp (x+y)+\2 answers -
3 answers
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0 answers
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2. Suppose that \( x^{3}-x \ln y+y^{3}=2 x+5 \). Find \( d y / d x \). 3. Find the derivative \( y^{\prime} \) : (a) \( y=\arctan \left(t^{2} e^{t}\right) \) (b) \( y=1+\left(\arcsin (x)^{2}\right) \)2 answers -
Evaluate the double integral. \[ \iint_{D} \frac{y}{x^{2}+1} d A, \quad D=\{(x, y) \mid 0 \leq x \leq 2,0 \leq y \leq \sqrt{x}\} \]2 answers -
11. Find \( \frac{d y}{d x} \). \[ \csc y+3 x=y^{2} \] [A] \( \frac{3}{2 y+\sec y \cot y} \) [B] \( \frac{3 y}{y+2 \csc y \cot y} \) [C] \( \frac{3 x}{2 y-\csc y \cot y} \) [D] \( \frac{3}{2 y+\csc y2 answers -
15. Find the second derivative, \( y^{\prime \prime} \), for the function \( y=\tan x \). [A] \( 2 \cdot \sec x \cdot \tan x \) [B] \( \sec ^{2} x \) [C] \( 2 \cdot \sec ^{2} x \cdot \tan x \) [D] \(2 answers -
ASAP WRITE CLEARLY
9. Solve the initial-value problem \[ x \frac{d y}{d x}=y+\sqrt{x^{2}-y^{2}}, \quad y(1)=0 . \] A. \( y=\sqrt{x-1}+\ln (x)-\sin (\pi x) \) B. \( y=\sin (\pi x) \) C. \( y=x \sin (\ln x) \) D. \( y=\ta2 answers -
2 answers
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Given \( f(x, y)=-6 x^{5}+3 x^{2} y^{6}-3 y^{2} \), find \[ f_{x}(x, y)= \] \[ f_{y}(x, y)= \] \[ f_{x x}(x, y)= \] \[ f_{x y}(x, y)= \]2 answers -
Halle la derivada de la función: \[ y=\frac{3 s^{2}+4 s-8}{s^{3 / 2}} \] a \[ y=\frac{3}{2} s^{-1 / 2}-2 s-322+24 s-5 / 2 \] \( y=\frac{3}{2} x^{1 / 2}-2 s-3 / 2+12,-5 / 2 \) \[ y=\frac{3}{2} s^{1 /2 answers -
3. Find the derivative of \( y \). (a) \( y=\arccos (1 / x) \) (c) \( y=\tan ^{-1}(\ln x) \) (b) \( y=\ln \left(\tan ^{-1} x\right) \) (d) \( y=\cos (x-\arccos x) \)2 answers -
Find the gradient vector field of \( f \), \[ f(x, y)=\ln (x+2 y) \] A. \( \nabla f(x, y)=\frac{1}{x+2 y} \hat{i}-\frac{2}{x+2 y} \hat{j} \) B. \( \nabla f(x, y)=\frac{1}{2 y} \hat{i}+\frac{2}{x+2 y}2 answers -
7. If \( y=6 x^{5}-2 x^{2}+9 x-3 \) find: a) \( y^{\prime} \) b) \( y^{\prime \prime} \) c) \( y^{\prime \prime \prime} \) d) \( \frac{d y}{d x} \) e) \( \frac{d^{2} y}{d x^{2}} \) f) \( \frac{d^{3} y2 answers -
11. Evaluate \( \iiint_{E} x d V \), where \( E=\{(x, y, z) \mid 0 \leq x \leq y, 0 \leq y \leq 1,0 \leq z \leq 2\} \).2 answers -
Solve the following differential equations by separation of variables: a. \( y^{\prime}=\frac{t^{2}}{y} \) b. \( \quad 4 t d y=\left(y^{2}+t y^{2}\right) d t \quad y(1)=1 \) c. \( y^{\prime}=\frac{2 t2 answers -
2 answers
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Find the first partial derivatives of the function. \[ f(x, y)=\frac{x}{y} \] \[ f_{x}(x, y)= \] \[ f_{y}(x, y)= \]2 answers -
Express the iterated integral in the opposite order. \[ \int_{0}^{7} \int_{e^{x}}^{e^{7}} f(x, y) d y d x= \] \[ \begin{array}{l} \int_{1}^{e^{7}} \int_{7}^{\ln y} f(x, y) d x d y \\ \int_{1}^{e^{7}}4 answers -
Determinar cuál de las siguientes series converge. \[ \sum_{n=1}^{\infty}\left(4+(-1)^{n}\right)^{n} \] \[ \sum_{n=0}^{\infty} 5\left(\frac{3}{2}\right)^{n} \] \[ \sum_{n=1}^{\infty} \frac{1}{\sqrt{n2 answers -
Evaluate \( \frac{d}{d x}\left(3 x^{2}+5\right) e^{-x} \) at \( x=0 \) \[ \left.\frac{d}{d x}\left(3 x^{2}+5\right) e^{-x}\right|_{x=0}= \] \( \frac{d}{d x} e^{5 x^{2}+6 x}= \)2 answers -
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}}{\s2 answers -
2 answers
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\( \iiint_{\mathcal{W}} \frac{z}{x^{2}+z^{2}} d V \) where \( \mathcal{W}=\{(x, y, z): 1 \leq y \leq 4, y \leq z \leq 4,0 \leq x \leq z\} \)2 answers -
2 answers
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( 1 point) Find \( y \) as a function of \( t \) if \[ y^{\prime \prime}+4 y=0 \] \[ \begin{array}{l} y(0)=4, \quad y^{\prime}(0)=2 \\ y= \end{array} \]2 answers