Calculus Archive: Questions from November 05, 2023
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Find the particular solution. \[ \begin{array}{l} y^{\prime \prime}+16 y=0, y(0)=2, y^{\prime}(0)=-2 \\ \bigcirc y=\sqrt{3} e^{-2 x}+e^{2 x} \\ \bigcirc=2 \sin (4 x)-\frac{1}{2} \sin (4 x) \\ y=\frac{1 answer -
1. Evaluate the following integrals: TT/2 [C sin y cos rv1+ cos² rdady; TV
Evaluate the following integrals: \[ \int_{0}^{1} \int_{\sin ^{-1} y}^{\pi / 2} \cos x \sqrt{1+\cos ^{2} x} d x d y \]1 answer -
Solve the given differential equation. \[ \begin{array}{l} \frac{d^{2} y}{d x^{2}}+36 y=\cos 6 x \\ y=c_{1} \sin 6 x+c_{2} \cos 6 x+\frac{1}{12} x \sin 6 x \\ y=c_{1} \sin 6 x+c_{2} \cos 6 x+\frac{1}{1 answer -
All same problem to bug to put in one photo though! so 3 cropped photos
\[ \begin{array}{l} g_{1}(z)= \\ g_{2}(z)= \\ h_{1}(y, z)= \\ h_{2}(y, z)= \\ \text { 4. } \int_{a}^{b} \int_{g_{1}(y)}^{g_{2}(y)} \int_{h_{1}(y, z)}^{h_{2}(y, z)} f(x, y, z) d x d z d y \\ a= \\ b= \0 answers -
i need the answer for question 3 and 4
Determine los puntos criticos de la función y utlice los criterios estudiados para clasificarlo(s) como un máximo, minimo o punto de silla. 1) \( f(x, y)=2 x y-\frac{1}{2}\left(x^{4}+y^{4}\right)+11 answer -
Solve the given differential equation. \[ \begin{array}{l} \frac{d^{2} y}{d x^{2}}+16 y=\cos 4 x \\ y=c_{1} \sin 4 x+c_{2} \cos 4 x+\frac{1}{8} x \sin 4 x \\ y=c_{1} \sin 4 x+c_{2} \cos 4 x+\frac{1}{81 answer -
Solve the given differential equation. \[ \begin{aligned} 3 y^{\prime \prime}-4 y^{\prime}+4 y & =0 \\ y & =e^{2 x / 3}\left(c_{1} \sin \frac{2 \sqrt{2}}{3} x+c_{2} \cos \frac{2 \sqrt{2}}{3} x\right)1 answer -
help on 11,14,15,16
11-18 Find the differential of the function. 11. \( y=e^{5 x} \) 12. \( y=\sqrt{1-t^{4}} \) 13. \( y=\frac{1+2 u}{1+3 u} \) 14. \( y=\theta^{2} \sin 2 \theta \) 15. \( y=\frac{1}{x^{2}-3 x} \) 16. \(1 answer -
help on 14 and 16 plz
11-18 Find the differential of the function. 11. \( y=e^{5 x} \) 12. \( y=\sqrt{1-t^{4}} \) 13. \( y=\frac{1+2 u}{1+3 u} \) 14. \( y=\theta^{2} \sin 2 \theta \) 15. \( y=\frac{1}{x^{2}-3 x} \) 16. \(1 answer -
openstax3.2: Problema 9 (1 punto) Resultados Tu respuesta NO es correcta. Find the value of \( \int_{0}^{\pi / 3} \sin (2 x) \sin (x) d x \).1 answer -
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Find \( y^{\prime} \) and \( y^{\prime \prime} \). \[ y=\ln (5+\ln (x)) \] \[ y^{\prime}= \] \[ y^{\prime \prime}= \]1 answer -
9) Si \( K \in \mathbb{N} \) y \( \left(a_{n}\right)_{n} \) es creciente, entonces \( a_{K} \leq a_{n} \forall n>K \) ?1 answer -
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Differentiate the function. \[ y=\left(6 x^{2}-3\right)\left(9 x^{2}-7 x+5\right) \] \[ \frac{d y}{d x}= \]1 answer -
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I.- Calcula la longitud de arco para cada una de las funciones y plantea la integral para obtener el valor exacto de la longitud de arco. a)𝑦 = 𝐿𝑛𝑥 desde el punto (1,0) hasta el punto (3,
\( y=\sqrt{x} \) desde el punto \( (0,0) \) hasta el punto \( (4,2) \) \( y=\frac{x^{4}}{8}+\frac{1}{4} x^{-2} \) desde \( x=1 \) hasta \( x=2 \) \( y=\operatorname{Ln}(\csc x) \) desde \( x=\1 answer -
Calcula de forma aproximada el área de la región limitada y plantea la integral que obtiene de forma exacta el valor del área. a) b) c)
\( (1,0) \) \( y=\operatorname{sen}(\pi \sqrt{x}) \) La región limitada por la función \( y^{3}=4 x, x=0 \) y \( x=-2 \), \( (1,0) \) La región limitada por la función \( y^{3}=4 x, x=0 \) y1 answer -
Use logarithmic differentiation to find \( y^{\prime} \). \[ y=\frac{\sqrt{4-7 x}\left(x^{2}+1\right)^{2}}{x^{2}+7 x+7} \] \[ y^{\prime}= \]1 answer -
3-32 Differentiate the function please I need help with 7,14,19,22
3-32 Differentiate the function. 3. \( f(x)=2^{40} \) 4. \( f(x)=e^{5} \) 5. \( f(x)=5.2 x+2.3 \) 6. \( g(x)=\frac{7}{4} x^{2}-3 x+12 \) \( f(t)=2 t^{3}-3 t^{2}-4 t \) 8. \( f(t)=1.4 t^{5}-2.5 t^{2}+61 answer -
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same questions but too long to put in one pic. so I had to crop it!
\[ \begin{array}{ll} g_{1}(z)= & g_{2}(z)= \\ h_{1}(y, z)= & h_{2}(y, z)= \end{array} \] 4. \( \int_{a}^{b} \int_{g_{1}(y)}^{g_{2}(y)} \int_{h_{1}(y, z)}^{h_{2}(y, z)} f(x, y, z) d x d z d y \) \[ \be1 answer -
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1. Find and classify any stationary points of the following functions: i) \( y=4 x^{2}+3 \) ii) \( y=x^{3}-3 x^{2}-24 x+15 \) iii) \( y=(2 x-1)^{2} \) iv) \( y=4 \sqrt{x}-2 x \) v) \( y=2 x^{3} \) vi)1 answer -
Given the equation \( y=\sin 3 x \), find \( y^{\prime \prime \prime} \). \[ \begin{aligned} y^{\prime \prime \prime} & =81 \sin 3 x \\ y^{\prime \prime \prime} & =-27 \cos 3 x \\ y^{\prime \prime \pr1 answer -
Determine if quadratic form is positive/negative definite: Determine si forma cuadrática es positiva/negativa definida:
Determine si forma cuadrática es positiva/negativa definida: 1. \( f\left(x_{1}, x_{2}\right)=4 x_{1}^{2}+3 x_{1} x_{2} \)1 answer -
Determine if quadratic form is positive/negative definite: Determine si forma cuadrática es positiva/negativa definida:
\( f\left(x_{1}, x_{2}, x_{3}\right)=\left(x_{1}, x_{2}, x_{3}\right)\left(\begin{array}{ccc}3 & 1 & 0 \\ 1 & 2 & -1 \\ 0 & -1 & 4\end{array}\right)\left(\begin{array}{l}x_{1} \\ x_{2} \\ x_{3}\end{ar1 answer -
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15x+3 x-∞ √36x²+2 2.) lim 3.) lim X→∞0 4.) lim sin x x² 5.) lim X->-00 3x³-2x²+5 22+1 4x 12x+sinx Sin X X➜-8 **Please solve all 4 with steps**
2.) \( \lim _{x \rightarrow-\infty} \frac{15 x+3}{\sqrt{36 x^{2}+2}} \) 3.) \( \lim \frac{\sin x}{x^{2}} \) \[ x \rightarrow \infty \] 4.) \( \lim \frac{3 x^{3}-2 x^{2}+5}{x^{2}+1} \) \[ x \rightarrow1 answer -
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1-8 differentiate find the derivative and simplify
\( \begin{array}{l}y=\frac{1}{3}\left(4+x^{4}\right)^{3} \\ z=\sqrt[4]{v+2}\end{array} \) \( y=\frac{4}{\sqrt{2 x^{2}-1}} \) \( y=x(x-1)^{4} \) \( y=2 x^{4}(x+2)^{2} \) \( y=3 x^{3}(x-1)^{3} \) \( y=41 answer -
If \( f(x, y) \) is a potential function for \[ \mathbf{F}(x, y)=e^{y} \mathbf{i}+\left(x e^{y}+3\right) \mathbf{j} \] evaluate \[ f(e, 2)-f(0,1) . \] 1. \( f(e, 2)-f(0,1)=3 e^{3}+1 \) 2. \( f(e, 2)-f1 answer -
9. \( y=\sin x, y=0,0 \leqslant x \leqslant \pi ; \) about \( y=-2 \) 5-10 Set up, but do not evaluate, an integral for the volume of the solid obtained by rotating the region bounded by the given2 answers -
(1 point) Find \( f^{\prime}(x) \) for \[ f(x)=-\frac{13 \sin (x)}{6 x^{2}-13 \sin (x)} \] \[ f^{\prime}(x)= \]1 answer -
Un fabricante produce televisores a un costo de 250 dólares cada uno y estima que si se venden a \( x \) dólares cada uno, los consumidores comprarán \( 300-x \) televisores por día. ¿A qué prec1 answer -
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2. Find lim x-0 sin 3x sin 5x x2 Thanks!
2. Find \( \lim _{x \rightarrow 0} \frac{\sin 3 x \sin 5 x}{x^{2}} \)1 answer -
13.1 (22, 24, 26, 28) Find the domain and range of the functions.
Finding the Domain and Range of a Function In Exercises 21-32, find the domain and range of the function. 21. \( f(x, y)=3 x^{2}-y \) 22. \( f(x, y)=e^{x y} \) 23. \( g(x, y)=x \sqrt{y} \) 24. \( g(x,1 answer -
Evaluate \[ \begin{array}{l} \int_{0}^{3} \int_{0}^{2} \int_{0}^{1}(x+y+z) d x d z d y \\ \int_{0}^{1} x+y+z \end{array} \]1 answer -
variación de parámetros paso por paso por favor
\( 26 \cdot 2 y^{\prime \prime}+2 y^{\prime}+y=4 \sqrt{x} \)1 answer -
Calcula las siguientes integrales. En este caso, debes de obtener primero una expresión/fórmula matemática (antiderivada), y después evaluar esta en los límites de integración. Nota: Debes de ha
18.- \( \int_{1.17741}^{1.51743} x \exp \left(x^{2}\right) \mathrm{d} x \quad \) Nota: Utiliza el cambio de variable \( u=x^{2} \) 19.- \( \quad \int_{0}^{1} \frac{4}{\pi} \frac{s}{\sqrt{1-s^{4}}} \ma1 answer -
Encontrar la solución particular
\( \frac{\mathrm{d}^{2} y}{\mathrm{~d} t^{2}}+5 \frac{\mathrm{d} y}{\mathrm{~d} t}+4 y=t^{2} e^{7 t} \)1 answer -
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12. Establish the identity. \[ \begin{array}{l} \frac{\sin \theta-\sin (30)}{2 \sin \theta}=-\cos (20) \\ \sin \theta-\sin (3 \theta)=-2 \cos (2 \theta) \sin \theta \\ \sin \theta-\sin (3 \theta)=-2\l1 answer -
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INTEGRALES Y DERIVADAS Necesito procedimientos completos, por favor.
1.- El conductor de un autom6vil que se desplaza en línea recta a velocidad constante de \( 60 \mathrm{mi} / \mathrm{h} \) después de 10 minutos de avanzar se detiene un mirador . ¿Cuántos pies re1 answer -
Given \( \cos (x+y)=\sin x \sin y \), find \( d y / d x \) by implicit differentiation. \[ \begin{array}{l} \frac{\sin (x+y)+\cos x \sin y}{\sin (x+y)+\sin x \cos y} \\ -\frac{\cos (x+y)+\cos x \sin y1 answer -
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Calculate d²y dx² = d²y dx² 19:105-10.0 y = -4x² + 5x
Calculate \( \frac{d^{2} y}{d x^{2}} \) \[ \begin{array}{l} y=-4 x^{2}+5 x \\ \frac{d^{2} y}{d x^{2}}=\square \end{array} \]1 answer -
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Find all the second partial derivatives. \[ \begin{array}{l} f(x, y)=x^{4} y-2 x^{3} y^{2} \\ f_{x x}(x, y)= \\ f_{x y}(x, y)= \\ f_{y x}(x, y)= \\ f_{y y}(x, y)= \end{array} \]1 answer -
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10. \( y=\sin x, \quad y=2 x / \pi, \quad x \) 11. \( x=1-y^{2}, \quad x=y^{2}-1 \) 12. \( 4 x+y^{2}=12, \quad x=y \)0 answers