Calculus Archive: Questions from October 11, 2023
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36. Longitud de arco de un sector circular Encuentre la longitud de arco desde \( (-3,4) \) hasta \( (4,3) \) en sentido horario a lo largo del círculo \( x^{2}+y^{2}=25 \). Demuestre que el resultad1 answer -
Calcular el área de una superficie de revolución En el ejercicio 37 , configure y evalúe la integral definida para el área de la superficie generada al girar la curva del eje \( x \). 37. \( y=\fr1 answer -
55. Área de la superficie lateral de un cono Un cono circular recto se genera al girar la región acotada por \( y=\frac{3 x}{4}, y=3 \) y \( x=0 \) respecto al eje \( y \). Encuentre el área de la1 answer -
4. Calculate \( y^{\prime} \) and \( y^{\prime \prime} \) if \[ e^{x^{2}+2 x y}=2 x^{2}-\sin ^{2}\left(x y^{2}\right) \]0 answers -
i am stuck on problems 12, 16 and 18. so if you could do one or all those problems i would be very grateful.
Calculating First-Order Partial Derivatives In Exercises 1-22, find \( \partial f / \partial x \) and \( \partial f / \partial y \). 1. \( f(x, y)=2 x^{2}-3 y-4 \) 2. \( f(x, y)=x^{2}-x y+y^{2} \) 3.1 answer -
5) \( \int_{0}^{1} \frac{d x}{\sqrt{81-x^{2}}} \) A) \( \sin ^{-1} \frac{1}{9} \) B) \( \frac{1}{9} \sin ^{-1} \frac{1}{9} \) \( \cos ^{-1} \frac{1}{9} \) D) \( 9 \cos ^{-1} \frac{1}{9} \) 6) \( \int1 answer -
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Solve the differential equation. y' = 38y² sin (r) y = y = 1 38 sin (r) + C y= 1 38 cos (x) + C y = 2 y=0 1 38 sin (r) + C
Solve the differential equation. \[ y^{\prime}=38 y^{2} \sin (x) \] \[ y=\frac{1}{38 \sin (x)+C} \] \[ y=\frac{1}{38 \cos (x)+C} \] \[ y=-\frac{1}{38 \sin (x)+C} \] \[ y=2 \] \[ y=0 \]1 answer -
Evaluate the double integral over the rectangular region R.
\( \begin{array}{l}\text { 16. } \iint_{R}(x \sin y-y \sin x) d A \\ R=\{(x, y): 0 \leq x \leq \pi / 2,0 \leq y \leq \pi / 3\}\end{array} \)1 answer -
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1. \( y=\cos (\tan (x)) \) 2. \( y=\sin (x) \tan (x) \) 3. \( y=\cos ^{3}(x) \) 4. \( y=\tan (x) \) A. \( y^{\prime}=-3 \cos ^{3}(x) \tan (x) \) B. \( y^{\prime}=1+\tan ^{2}(x) \) C. \( y^{\prime}=\si1 answer -
1. (20 points) Differentiate a) \( y=\left(5 x^{4}+2 x^{3}\right)^{406} \) b) \( f(x)=\left(3 x^{2}-5 x\right) e^{\prime} \) c) \( y=\cot (\sin \theta) \) d) \( y=e^{\sqrt{6}} \) e) \( y=\frac{x}{2-\t1 answer -
\( \begin{array}{l}\text { Evaluate } \int_{C} \mathbf{F} \cdot d \mathbf{r} \\ \qquad \begin{array}{l}\mathbf{F}(x, y)=x \mathbf{i}+y \mathbf{j} \\ C: \mathbf{r}(t)=(7 t+5) \mathbf{i}+t \mathbf{j}, \1 answer -
1) If \( f(x, y)=\frac{\sqrt{4-x^{2}}}{y^{2}+3} \) A) Find \( f(2,3) \). B) Describe the domain of \( f \) ?1 answer -
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Solve X = 0 y = 0 = 2 0 W = X X - Y Y + 2y ++ - 22 W 2z + W - ++ -2 3z + W 5w - = 1 2 Ν 1 2
Solve \[ \begin{array}{r} x-y+z-w=1 \\ y+2 z+w=2 \\ -z+w=1 \\ -x+2 y-3 z+5 w=2 \end{array} \] \[ x=\quad y=\quad z=\quad, w= \]1 answer -
30. tan 0 √1-12 dA, R = {(0, t) | 0 ≤ 0 ≤ π/3,0 ≤ t ≤}}}
30. \( \iint_{R} \frac{\tan \theta}{\sqrt{1-t^{2}}} d A, \quad R=\left\{(\theta, t) \mid 0 \leqslant \theta \leqslant \pi / 3,0 \leqslant t \leqslant \frac{1}{2}\right\} \)1 answer -
is this correct? z = xy^4, x = e^-t, y = sint
\( \begin{aligned} \frac{d z}{d t} & =\frac{\partial z}{\partial x} \cdot \frac{d x}{d t}+\frac{\partial z}{\partial y} \cdot \frac{d y}{d t} \\ z & =x y^{4}, x=e^{-t}, y=\sin t \\ \frac{d z}{d t} & =1 answer -
I.Find the derivative of each of the following functions. 1. \( y=x^{3}-4 x^{2}+7 x-5 \) \( 3 x^{2}-8 x+7 \) 2. \( y=\frac{3 x^{3}-2 x+5}{x^{2}} \) 3. \( y=4 \sqrt{x}-\frac{6}{x^{2} \sqrt{x}} \) 4. \(1 answer -
6,7,9,12,13,15,16,17,18,19,20,22
1-22 Differentiate. 1. \( f(x)=3 \sin x-2 \cos x \) 2. \( f(x)=\tan x-4 \sin x \) 3. \( y=x^{2}+\cot x \) 4. \( y=2 \sec x-\csc x \) 5. \( h(\theta)=\theta^{2} \sin \theta \) 6. \( g(x)=3 x+x^{2} \cos1 answer -
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Evaluate the integral. \[ \int \sin 7 t \sin 3 t d t \] \[ \frac{1}{8} \sin 4 t-\frac{1}{20} \] (B) \( \frac{1}{8} \sin 4 t+\frac{1}{20} \) C) \( \frac{1}{8} \sin 4 t-\frac{1}{20} \) (D) \( \frac{1}{81 answer -
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\( \begin{array}{l}\text { If } f(x)=\frac{\tan x-3}{\text { sec } x} \\ f^{\prime}(x)= \\ f^{\prime}(5)=\end{array} \)1 answer -
Evaluate the integral. \[ \int \frac{\cos y d y}{\sin ^{2} y+\sin y-6} \] \[ \int \frac{\cos y d y}{\sin ^{2} y+\sin y-6}= \] (Type an exact answer.)1 answer -
2. Encuentre un vector unitario en la dirección de \( \vec{v}=2 i+j+2 k \) a. \( \vec{u}=\frac{2}{\sqrt{5}} i+\frac{1}{\sqrt{5}} j+\frac{1}{\sqrt{5}} k \) b. \( \vec{u}=\frac{2}{9} i+\frac{1}{9} j+\f1 answer -
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5,7,9,and 13 please
Find the area between the curves in Exercises 1-28. 1. \( x=-2, \quad x=1, \quad y=2 x^{2}+5, \quad y=0 \) 2. \( x=1, \quad x=2, \quad y=3 x^{3}+2, \quad y=0 \) 3. \( x=-3 . \quad x=1 . \quad y \quad1 answer -
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(9 pt) 8. If \( u=f(x, y) \), where \( x=e^{s} \cos t \) and \( y=e^{s} \sin t \), show that \( u_{x}^{2}+u_{y}^{2}=e^{-2 s}\left(u_{s}^{2}+u_{t}^{2}\right) \).1 answer -
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solución de un sistema de ecuaciones lineales x=-e^t y=e^t
A. En los problemas del 1 al 4, verifique que el par de funciones dado sea una solución para el sistema de primer orden. 1. \[ \begin{array}{l} x=-e^{t}, \quad y=e^{t} \\ \frac{d x}{d t}=-y, \quad \f0 answers -
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Find \( \frac{d^{2} y}{d x^{2}} \). \[ y=\frac{1}{x^{2}-1} \] A. \( \frac{6 x^{2}-2}{\left(x^{2}-1\right)^{3}} \) B. \( \frac{6 x^{2}+2}{\left(x^{2}-1\right)^{3}} \) C. \( \frac{6 x^{2}+2}{\left(x^{2}1 answer -
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1, 3, and 5 please!
In Exercises \( 1-8 \), evaluate \( \iiint_{\mathscr{X}} f(x, y, z) d V \) for the specified function \( f \) and box \( \mathscr{B} \). 1. \( f(x, y, z)=x z+y z^{2} ; \quad 0 \leq x \leq 2, \quad 2 \1 answer -
13 amd 14 please!
In Exercises 9-14, evaluate \( \iiint_{\mathscr{E}} f(x, y, z) d V \) for the function \( f \) and region \( \mathscr{W} \) specified. 9. \( f(x, y, z)=x+y ; \quad \mathscr{W}: y \leq z \leq x, \quad1 answer -
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Find the derivative. y' = y = 10t² + 12 8 √t t²
Find the derivative. \[ y=10 t^{2}+\frac{12}{\sqrt{t}}-\frac{8}{t^{2}} \] \[ y^{\prime}= \]1 answer -
1. \( \left(D^{4}-49 D^{2}\right) y=e^{7 x}+\cos (7 x+3)-7 x^{3}+2 \) 2. \( (2+3 x)^{2} \cdot \frac{d^{2} y}{d x^{2}}+3(2+3 x) \cdot \frac{d y}{d x}-36 y=x^{2}+6 x+1+4 \cos \ln (2+3 x) \)1 answer -
Solve the following initial value problems: (a) \[ y^{\prime \prime}+2 y^{\prime}+145 y=0 ; \quad y(0)=3, y^{\prime}(0)=1 \] (b) \[ y^{\prime \prime}+2 y^{\prime}+145 y=1 ; \quad y(0)=0, y^{\prime}(0)1 answer -
32. Determine si las siguientes funciones tienen límite en el punto que se indica. Pruebe su respuesta. 5 iii) \( f(x, y)=\frac{x^{2}(y-1)}{x^{4}+(y-1)^{2}} \quad \) en \( (0,1) \quad 50 \) iv) \( f1 answer -
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9. Sean \( f: U \subset \mathbb{R}^{n} \rightarrow \mathbb{R}, \hat{x}_{0} \in U,(a, b) \subset \mathbb{R} \) tal que \( f(U) \subset(a, b) \) y \( g:(a, b) \subset \mathbb{R} \rightarrow \mathbb{R} \1 answer -
Compute the gradient vector fields of the following functions: \begin{tabular}{|c|c|c|c|} \hline \multicolumn{4}{|c|}{ A. \( f(x, y)=10 x^{2}+5 y^{2} \)} \\ \hline\( \nabla f(x, y)= \) & \( \mathbf{i}1 answer -
Find y' and y". y' = y" = = y = In(sec 5x + tan 5x)
Find \( y^{\prime} \) and \( y^{\prime \prime} \). \[ y=\ln (\sec 5 x+\tan 5 x) \] \[ y^{\prime}= \] \[ y^{\prime \prime}= \]1 answer -
Differentiate the function. y = √2 + 4e6x y' =
Differentiate the function. \[ y=\sqrt{2+4 e^{6 x}} \] \[ y^{\prime}= \]1 answer -
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Differentiate. \[ y=\frac{x+1}{x^{3}+x-8} \] Differentiate, \[ y=\frac{7-\sec (x)}{\tan (x)} \] \[ y^{\prime}= \]1 answer -
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Trazar la media proporcional en el Teorema de la Altura y el Teorema de Cateto
II. Traza la media proporelonal con el Teoremn de la Altura y Teorema del Cetato. (Aotis, Cu, Lotal bots.) 7) \( \pi B=6 \quad T C=3 \) 8) \( \overline{X I}=4 \overline{D C}=6 \) III. Obtén la raiz n0 answers -
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Ejercicios: 1) Determine masa y el centro de masa del sólido con densidad dada acotado por las gráficas de las ecuaciones. Establezca y evalúe claramente el integral triple que permite determinarlo
Ejercicios: 1) Determine masa y el centro de masa del sólido con densidad dada acotado por las gráficas de las ecuaciones. Establezca y evalúe claramente el integral triple que permite determinarlo1 answer -
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In Exercises 5-24, compute the derivative. 5. \( f(x)=\sin x \cos x \) 6. \( f(x)=x^{2} \cos x \) 7. \( f(x)=x \sin x \) 8. \( f(x)=9 \sec x+12 \cot x \) 9. \( H(t)=\sin t \sec ^{2} t \) 10. \( h(t)=91 answer