Calculus Archive: Questions from April 15, 2023
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Solve the ODE
6. \( y^{\prime \prime}=-y \) 7. \( y^{\prime}=\cosh 5.13 x \) 8. \( y^{\prime \prime \prime}=e^{-0.2 x} \)2 answers -
\( \int 6 x \sin 3 x d x= \) (A) \( -\frac{6}{3} x \cos 3 x-\frac{6}{3^{2}} \sin 3 x+C \) (B) \( -\frac{6}{3} x \cos 3 x+\frac{6}{3} \cos 3 x+C \) (C) \( -\frac{6}{3} x \cos 3 x+\frac{6}{3} \sin 3 x+C2 answers -
\( \int 6 x \sin 8 x d x= \) (A) \( -\frac{6}{8} x \cos 8 x+\frac{6}{8} \cos 8 x+C \) (B) \( -\frac{6}{8} x \cos 8 x+\frac{6}{8^{2}} \sin 8 x+C \) (C) \( -\frac{6}{8} x \cos 8 x+\frac{6}{8^{2}} \cos 82 answers -
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21-26 . Calculate the double integral. 21. \( \iint_{R} \frac{x y^{2}}{x^{2}+1} d A, \quad R=\{(x, y) \mid 0 \leqslant x \leqslant 1,-3 \leqslant y \leqslant 3\} \)2 answers -
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Objetivo: Esta actividad tiene como propósito ayudar al estudiante a determinar una solución particular para una integral indefinida y a determinar el valor promedio de una integral definida. (0bjet0 answers -
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\[ \int \sin ^{3} x d x \] A) \( \cos x-\frac{\sin ^{3} x}{3}+c \) B) \( -\cos x+\frac{\cos ^{3} x}{3}+c \) \( -\cos x-\frac{\cos ^{3} x}{3}+c \) D) \( \sin x-\frac{\sin ^{3} x}{3}+\mathrm{c} \) B C D2 answers -
Find the general solution of the equation. \[ y^{\prime}(x)=y-21 \] A) \( y=C e^{x}+21 \) B) \( y=C e^{x}-21 \) C) \( y=C e^{21 x} \) D) \( y=C e^{21 x}-21 \)2 answers -
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Evaluate the triple integral \( \iiint_{E} y d V \) where \( E=\{(x, y, z) \mid 0 \leq x \leq 3, \quad 0 \leq y \leq x, \quad x-y \leq z \leq x+y\} \) Solve it by writing it as an iterated integral fi2 answers -
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Solve the following initial value problem. \[ \left(e^{-2 \sqrt{x}}-y\right) \mathrm{d} x-\sqrt{x} \mathrm{~d} y=0, \quad y(1)=1 \] Solution: \[ y=2 \sqrt{x} e^{-2 \sqrt{x}}+\left(e^{2}-2\right) e^{-22 answers -
Solve the following initial value problem. \[ y^{\prime \prime}+3 y^{\prime}+2 y=\frac{e^{-x}}{2+e^{x}}, \quad y(0)=0, \quad y^{\prime}(0)=1 \] Solution: \[ y=\frac{1}{2} e^{-2 x}\left[e^{x}(x+2+\ln 32 answers -
If \( \sum_{k=1}^{n} a_{k}=4 \) and \( \sum_{k=1}^{n} b_{k}=12 \), find the following values. \[ \sum_{\substack{k=1 \\ n}}^{n} 9 a_{k}, \sum_{k=1}^{n} \frac{b_{k}}{12}, \sum_{k=1}^{n}\left(a_{k}+b_{k2 answers -
If \( \int_{1}^{7} f(x) d x=16 \) and \( \int_{6}^{7} f(x) d x=3.1 \), find \( \int_{1}^{6} f(x) d x \) Answer:2 answers -
Please help answering the following exercises:
\( \operatorname{Sea} f(x, y)=\int_{y}^{x} \cos \left(t^{2}\right) d t \) Luego, \( \frac{\partial f}{\partial y}(x, y)= \) a. \( -\cos (y) \operatorname{sen}(y) \) b. \( \cos \left(y^{2}\right) \) c.2 answers -
Prove the identity. \[ \begin{array}{l} \sinh (x+y)=\sinh (x) \cosh (y)+\cosh (x) \sinh (y) \\ \sinh (x) \cosh (y)+\cosh (x) \sinh (y)=\left[\frac{1}{2}\left(e^{x}-e^{-x}\right)\right]\left[\frac{1}{22 answers -
2. Multiplicadores de Lagrange. Encontrar la distancia mas corta desde el plano \( x+2 y+z=4 \) al origen. Nota: función a minimizar: distancia al cuadrado entre dos puntos.2 answers -
Find all the second partial derivatives. \[ \begin{array}{l} f(x, y)=x^{6} y^{4}+4 x^{5} y \\ f_{x x}(x, y)= \\ f_{x y}(x, y)= \\ f_{y x}(x, y)= \\ f_{y y}(x, y)= \end{array} \]2 answers -
Find all the second partial derivatives. \[ \begin{array}{l} f(x, y)=x^{6} y^{4}+4 x^{5} y \\ f_{x x}(x, y)= \\ f_{x y}(x, y)= \\ f_{y x}(x, y)= \\ f_{y y}(x, y)= \end{array} \]2 answers -
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please helpp
Evaluate \( \iiint_{B} f(x, y, z) d V \) for the specified function \( f \) and \( \mathcal{B} \) : \[ f(x, y, z)=\frac{z}{x} \quad 3 \leq x \leq 15,0 \leq y \leq 3,0 \leq z \leq 10 \] \[ \iiint_{B} f2 answers -
Si \( f(x, y)=x^{2} y^{3} \). ¿Cuál es el valor de \( f_{x}(2,1) \) ? Select one: a. 2 b. 4 c. 0 d. 1 Si \( f(x, y)=x^{2} \ln (x y) \). Entonces, \( \frac{\partial f}{\partial x}= \) Select one: a.2 answers -
Differentiation.
\( f(x)=\int_{0}^{x} 3 e^{-t^{2}} \) dt then \( d f / d x= \) \( y=x^{2}+c / x^{2} \) then \( x(d y / d x)+2 y= \)2 answers -
Find all possible functions with the given derivatives. a. \( y^{\prime}=6 x^{5} \) b. \( y^{\prime}=6 x^{5}-8 \) c. \( y^{\prime}=7 x^{6}+6 x^{5}-8 \)2 answers -
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