Calculus Archive: Questions from September 05, 2023
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1. Solve the differential equation if \( y(0)=1 \), and \( y^{\prime}(0)=2 \). \[ y^{\prime \prime}+6 y^{\prime}+9 y=\cos t \] 2. Solve the differential equation if \( y(0)=0, y^{\prime}(0)=0 \), and1 answer -
Alguien que me ayude por favor r Ecuacion 1: Ecuacion 2: Favor de ayudarme
Resuelva el siguiente ejercicio. Explique claramente lo que realiza. (20 puntos) a) Halle la pendiente de la línea tangente a la curva en el punto \( (3,2) \). \[ y=\frac{x-1}{x-2} \] Usando las ecua1 answer -
Let \( \mathbf{v}=\langle-2, \quad 1,-2\rangle \) Calculate: \[ \begin{array}{l} \mathbf{v} \times \mathbf{i}=\left\langle \_\right. \\ \mathbf{v} \times \mathbf{j}=\langle,\rangle \\ \mathbf{v} \time1 answer -
32. y = sec 33. y = sin x, x = 0, y = 0, and y T about the y-axis 4 T -1 x, x = 0, y == ; about the y-axis 4 question 33
32. \( y=\sec ^{-1} x, x=0, y=0 \), and \( y=\frac{\pi}{4} \); about the \( y \)-axis 33. \( y=\sin ^{-1} x, x=0, y=\frac{\pi}{4} \); about the \( y \)-axis0 answers -
Prove the convergence or divergence of the series. If it is convergent, find the sum.
Demuestre la convergencia o divergencia de las series. Si es convergente encuentre su suma. 1. \( \sum_{n=1}^{\infty}\left(1+\frac{2}{n}\right)^{n} \) 2. \( \sum_{n=0}^{\infty}\left(\frac{2}{3}\right)0 answers -
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Find \( \mathbf{a}+\mathbf{b}, 9 \mathbf{a}+7 \mathbf{b},|\mathbf{a}| \), and \( |\mathbf{a}-\mathbf{b}| \) \[ \mathbf{a}=9 \mathbf{i}-8 \mathbf{j}+7 \mathbf{k}, \quad \mathbf{b}=7 \mathbf{i}-9 \mathb1 answer -
\( \begin{array}{l}\text { Find } \mathbf{a}+\mathbf{b}, 9 \mathbf{a}+7 \mathbf{b},|\mathbf{a}| \text {, and }|\mathbf{a}-\mathbf{b}| \\ \qquad \mathbf{a}=9 \mathbf{i}-8 \mathbf{j}+7 \mathbf{k}, \quad1 answer -
Simplify. \[ \frac{\frac{x}{y}-\frac{y}{x}}{\frac{1}{y}+\frac{1}{x}} \] \[ \frac{\frac{x}{y}-\frac{y}{x}}{\frac{1}{y}+\frac{1}{x}}= \]1 answer -
5. Identify the horizontal asymptotes of \( f \). \[ f(x)=\frac{\sqrt{9 x^{4}+25 x}+x^{2}}{x^{2}-9} \] A. \( y=3 \) B. \( y=8 \) C. \( y=9 \) D. \( y=0 \) E. \( y=4 \)1 answer -
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hello i need help on 5,8,11 thank you
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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1. En un instante dado, la longitud de un cateto de un triángulo rectángulo es de 20cm y crece a la taza de 2 cm min. cm 24 cm y decrece a una tasa de 4 1.1 Realice el dibujo 1.2 min. y la longitud
1. En un instante dado, la longitud de un cateto de un triángulo rectángulo es de \( 20 \mathrm{~cm} \) y crece a la taza de \( 2 \frac{\mathrm{cm}}{\mathrm{min}} \), y la longitud del otro cateto e1 answer -
La temperatura de una bola en el punto \( P(x, y, z) \), con centro en el origen se modela mediante la función: \[ T(x, y, z)=100 /\left(2+x^{2}+y^{2}+z^{2}\right) . \] a. ¿Halle la dirección de ma1 answer -
25. 0 π/4 1 - sin²0 cos²0 de
25. \( \int_{0}^{\pi / 4} \frac{1-\sin ^{2} \theta}{\cos ^{2} \theta} d \theta \)1 answer -
PLEASE LOOK AT BOTH PHOTOS. Differentiate the function. y = O A. SOB. 7x²-1 4x³ +5 y' = y' = d d (7x² - 1) († (7x² - 1)) - (4x³ + 5) (4x²+5) dx (4x³ + 5)² (4x³+5) (x (7x² - 1)) - (7x² - 1
Differentiate the function. \[ y=\frac{7 x^{2}-1}{4 x^{3}+5} \] A. \( y^{\prime}=\frac{\left(7 x^{2}-1\right)\left(\frac{d}{d x}\left(7 x^{2}-1\right)\right)-\left(4 x^{3}+5\right)\left(\frac{d}{d x}\1 answer -
Differentiate the function. y = y' = 9x²-4 4x³ +7 XE
Differentiate the function. \[ y=\frac{9 x^{2}-4}{4 x^{3}+7} \]1 answer -
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30. Region between \( y=x \) and \( x+y=8 \) over \( [2,3] \) In Exercises 31-50, sketch the region enclosed by the curves and compute its area as an integral along the \( x \)-or \( y \)-axis. 31. \(1 answer -
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30. Region between \( y=x \) and \( x+y=8 \) over \( [2,3] \) In Exercises 31-50, sketch the region enclosed by the curves and compute its area as an integral along the \( x \)-or \( y \)-axis. 31. \(1 answer -
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30. Region between \( y=x \) and \( x+y=8 \) over \( [2,3] \) In Exercises 31-50, sketch the region enclosed by the curves and compute its area as an integral along the \( x \)-or \( y \)-axis. 31. \(1 answer -
Question 1: For the following functions, calculate the first derivative. a) \( y=f(x)=\operatorname{Ln} \sqrt{3 x+1} \) b) \( y=f(x)=\frac{\sqrt{2 x^{2}+3 x+1}}{x^{3}} \) c) \( y=f(x)=\frac{1}{2 \sqrt1 answer -
Finds the total differential:
Halle el diferencial total a) \( z=e^{x} \operatorname{sen}(y) \) b) \( w=\frac{x+y}{z-3 y} \)1 answer -
consider the function f(x,y)=ye x and work:
Considere la función \( f(x, y)=y e^{x} \) y trabaje: a) Evaluar \( f(2,1) \) y \( f(2.1,1.05) \) b) Calcular \( \Delta z=f(x+\Delta x, y+\Delta y)-f(x, y) \) c) usar el diferencial total \( d z \) p1 answer -
Find the derivative of \( y \) with respect to \( x \) for the following. 1. \( y=e^{-2 x / 3} \) 2. \( y=x e^{-2 x / 3} \) 3. \( y=(1+3 x) e^{-x} \) 4. \( y=\frac{e^{x}}{1+e^{x}} \) 5. \( y=\ln \left1 answer -
Encontrar el enésimo término de las sucesiones \[ \begin{array}{l} \frac{1}{4}, \frac{2}{9}, \frac{3}{16}, \frac{4}{25}, \ldots \\ a_{n}=1-\frac{3 n}{1^{n^{2}}} \\ a_{n}=\frac{1}{(n+1) !} \\ a_{n}=\1 answer -
Demuestra la convergencia o divergencia de las sucesiones. \[ \left\{\frac{n !}{(n-2) !}\right\} \] Converge a 2 Converge a 0 Converge a 4 Diverge Encontrar la suma de las series infinitas \[ \1 answer -
Sean f(x) y g(x) funciones, suponga que = y que – f(x)) = 2. Calcule los limites usando propiedades o reglas de los limites. Muestre sus cálculos. 4f(x) + 3g(x) x2 f(x) - g(x)
\( \frac{f(x)-4}{g(x)+5} \) \( \lim _{x \rightarrow 6} \) b) \( \lim _{x \rightarrow 6} \) \( \lim _{x \rightarrow 6}(g(x) \) \( \lim _{x \rightarrow 6} \) \( \frac{1}{2} \) \( \lim _{x \right0 answers -
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Find each limit. f(x, y) = 6x² + 5y² (a) (b) lim Ax → 0 lim Ay → 0 f(x + Ax, y) = f(x, y) Ax f(x, y + Ay) - f(x, y) Ay
Find each limit. \[ f(x, y)=6 x^{2}+5 y^{2} \] (a) \( \lim _{\Delta x \rightarrow 0} \frac{f(x+\Delta x, y)-f(x, y)}{\Delta x} \) (b) \( \lim _{\Delta y \rightarrow 0} \frac{f(x, y+\Delta y)-f(x, y)}{1 answer -
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\( y=\frac{\sec 2 \theta}{1+\tan 2 \theta} \) \( \begin{array}{l}y+x \cos y=x^{2} y \\ y=\left(1-x^{-1}\right)^{-1}\end{array} \)0 answers -
49-59. Revolution about other axes Let \( R \) be the region bounded by the following curves. Find the volume of the solid generated when \( R \) is revolved about the given line. 51. \( x=2-\sec y1 answer -
z = √25-x² - y² (x, y) varies between (1,1) to (1.01,0.97) - Given a function of 2 variables, calculate the increase in z and the differential in z (dz) when varying (x,y) - Determine the er
c. \( z=\sqrt{25-x^{2}-y^{2}} \quad(x, y) \) varia de \( (1,1) \) a \( (1.01,0.97) \) - Dada una función de 2 variables calcule el incremento en z \( (\Delta z) \) y el diferencial en \( z(d z) \) a0 answers -
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- Given a function of 2 variables, calculate the increase in z and the differential in z (dz) when varying (x,y) - Determine the error made by using dz instead of z Z= 25-x² - y² (x, y) varia de (1
\( z=\sqrt{25-x^{2}-y^{2}} \quad(x, y) \) varia de \( (1,1) a(1.01,0.97) \) Dada una función de 2 variables calcule el incremento en \( z(\Delta z) \) y el diferencial en \( z(d z) \) al variar \(0 answers