Calculus Archive: Questions from September 24, 2023
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1. Suponga que la función de densidad conjunta para variables aleatorias \( X, Y \) y Z es \[ \begin{array}{c} f(x, y, z)=C x y z \text { si } 0 \leq x \leq 2,0 \leq y \leq 2,0 \leq z \leq 2 y \\ f(x1 answer -
Check the correct form of the particular solution for \( y^{\prime \prime}+4 y^{\prime}+8 y=e^{2 x}+\sin (3 x)+(5 x+3) \cos (2 x) \) \( A \exp (2 x)+B \cos (3 x)+C \sin (3 x)+(D x+E) \cos (2 x)+(F x+G1 answer -
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1. Demuestre la convergencia o divergencia de la serie, utilizando el criterio de la razón \( \sum_{n=1}^{\infty} \frac{n !}{(n-4) !} \) a. Converge por el criterio de la razón b. Diverge por el cri1 answer -
Let \( F(x, y, z)=x^{3} y z^{2}-8 x^{2} y z+9 x z-3 y^{3} z \). Find \( F_{x y z} \). \[ F_{x y z}= \]1 answer -
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3. If \( y=e^{x^{2}+x} \), Show that (i) \( \quad y_{2}-(2 x+1) y_{1}+2 y=0 \) (ii) \( \quad y_{n+2}-(2 x+1) y_{n+1}-2(n+1) y_{n}=0 \).1 answer -
< Differentiate the function. y = 7x²-9 8x +3 y': -0
Differentiate the function. \[ y=\frac{7 x^{2}-9}{8 x^{3}+3} \] \[ y^{\prime}= \]1 answer -
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Find \( f_{x x}(x, y) \) for \( f(x, y)=\frac{9 x^{2}}{y}+\frac{y^{2}}{2 x} \). \[ f_{x x}(x, y)= \]1 answer -
Find all the second partial derivatives. \[ f(x, y)=x^{8} y^{9}+2 x^{6} y \] \[ f_{x x}(x, y)= \] \[ f_{x y}(x, y)= \] \[ f_{y x}(x, y)= \] \[ f_{y y}(x, y)= \]1 answer -
12. Estime la derivada numéricamente de la siguiente función en el punto especificado. 9. \( C(x)=10,000+5 x-\frac{x^{2}}{10,000} ; x=1,000 \)1 answer -
Use una calculadora gráfica para dibujar la región limitada por las gráficas de las ecuaciones 1. Encuentre el área de la región \( y=e^{-x} \sin \pi x, y=0, x=0 \quad y x=1 \) 2. Halle el volume1 answer -
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Express the integral \( \iiint_{E} f(x, y, z) d V \) as an iterated integral in six different ways, where \( \mathrm{E} \) is the solid bounded by \( z=0, x=0, z=y-4 x \) and \( y=8 \). \[ \begin{arra1 answer -
Express the integral \( \iiint_{E} f(x, y, z) d V \) as an iterated integral in six different ways, where \( \mathrm{E} \) is the solid bounded by \( z=0, z=2 y \) and \( x^{2}=36-y \). 1. \( \int_{a}1 answer -
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Find \( \frac{d y}{d x} \) for \( e^{x+4 y}=y \) Select one: a. \( \frac{e^{x+4 y}}{\left(1-4 e^{x+4 y}\right)} \) b. \( \frac{e^{x+4 y}}{\left(4 e^{x+4 y}-1\right)} \) c. \( e^{x+4 y} \) d. \( \frac{1 answer -
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Differentiate the following function. OA) OB) O c) OD) ƒ'(x) = ƒ'(x) = ƒ'(x) = D) f'(x) = ƒ(x) = e +tan(x) cos(x) cos(x) (e+cot²(x))+sin(x) (e*+tan(x)) cos² (x) cos(x) (eª+sec²(x))+sin(x)(eª+
Differentiate the following function. \[ f(x)=\frac{e^{x}+\tan (x)}{\cos (x)} \] A) \( f^{\prime}(x)=\frac{\cos (x)\left(e^{x}+\cot ^{2}(x)\right)+\sin (x)\left(e^{x}+\tan (x)\right)}{\cos ^{2}(x)} \)1 answer -
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7. Describe and sketch the domains of the following functions (a) h(x, y) = e√y-z² (b) f(x, y, z) = ln(z - 11 x² + y²) (c) f(x, y, z) = √4-x² +√9-y² + √1 - z²
7. Describe and sketch the domains of the following functions (a) \( h(x, y)=e^{\sqrt{y-x^{2}}} \) (b) \( f(x, y, z)=\ln \left(z-\sqrt{x^{2}+y^{2}}\right) \) (c) \( f(x, y, z)=\sqrt{4-x^{2}}+\sqrt{9-y1 answer -
Find y' and y'". area y" = y = 83e* Need Help?
Find \( y^{\prime} \) and \( y^{\prime \prime} \). \[ y=e^{3 e^{x}} \] \[ y^{\prime}= \]1 answer -
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18. \( f(x, y)=x^{3} y+\cos x ; D \) es el triángulo definido por \( 0 \leq x \leq \pi / 2,0 \leq y \leq x \).0 answers -
g(r) = (7r³ +5r+6)(r²+3) g'(r) =
\( g(r)=\left(7 r^{3}+5 r+6\right)\left(r^{2}+3\right) \) \( g^{\prime}(r)= \)1 answer -
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Differentiate the following function. f(x) = 2x³ + 6x L OD) f'(x) = 6x² +6+ E) f'(x) = 5x² + 6 − ○ A) ƒ'(x) = 6x² + 6+2+3xe-¹-cos(x) ○ в) ƒ'(x) = 6x² + 6−2+3e +cos(x) B) 1 1 X c) f'(x
Differentiate the following function. \[ f(x)=2 x^{3}+6 x-\frac{1}{x}+3 e^{x}-\sin (x) \] A) \( f^{\prime}(x)=6 x^{2}+6+\frac{1}{x^{2}}+3 x e^{x-1}-\cos (x) \) в) \( f^{\prime}(x)=6 x^{2}+6-\frac{1}{1 answer -
Find y' for y = 2x¯4 - 2x,1 y' =
Find \( y^{\prime} \) for \( y=2 x^{-4}-2 x^{-1} \) \[ y^{\prime}= \]1 answer -
Compute the derivatives indicated. \[ f(x, y)=5 x^{2} y-6 x y^{4}, \quad \frac{\partial^{2} f}{\partial x^{2}}, \quad \frac{\partial^{2} f}{\partial y^{2}} \] \[ \begin{array}{l} \frac{\partial^{2} f}1 answer -
El cálculo de la integral doble de la función f(x,y)=xy sobre la región dada a continuación es
El cálculo de la integral doble de la función \( f(x, y)=x y \) sobre la región dada a continuación es1 answer -
Determine \( f_{x y} f_{y y}-\left(f_{x y}\right)^{2} \) when \[ f(x, y)=\frac{2}{3} x^{3}+2 y^{2}+7 x+7 y+7 x y \text {. } \] 1. \( f_{x x} f_{y y}-\left(f_{x y}\right)^{2}=16 x+49 \) 2. \( f_{x x} f1 answer -
For \( f(x, y) \), find all values of \( x \) and \( y \) such that \( f_{x}(x, y)=0 \) and \( f_{y}(x, y)=0 \) simultaneously. \[ \begin{array}{l} f(x, y)=x^{2}+3 x y+y^{2}-26 x-24 y+50 \\ (x, y)=\le1 answer -
Find \( \partial y / \partial x_{1} \) and \( \partial y / \partial x_{2} \) for each of the following functions: (a) \( y=2 x_{1}^{3}-11 x_{1}^{2} x_{2}+3 x_{2}^{2} \) (c) \( y=\left(2 x_{1}+3\right)1 answer