Calculus Archive: Questions from April 20, 2023
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Find all possible functions with the given derivatives. a. \( y^{\prime}=6 x^{5} \) b. \( y^{\prime}=6 x^{5}+3 \) c. \( y^{\prime}=7 x^{6}-6 x^{5}+3 \)2 answers -
Find all possible functions with the given derivatives. a. \( y^{\prime}=5 x^{4} \) b. \( y^{\prime}=5 x^{4}-5 \) c. \( y^{\prime}=6 x^{5}+5 x^{4}-5 \) a. \( y= \) b. \( y= \) c. \( y= \)2 answers -
1. Para el campo vectorial \[ F(x, y)=y \hat{\imath}+x \hat{\jmath} \] (i) De una tabla de valores y grafique varios vectores que den una buena idea el campo. (ii) Las curvas de flujo se pueden obtene2 answers -
2. Para el campo vectorial \[ G(x, y)=\left\langle y^{2} \cos \left(x y^{2}\right), 2 x y \cos \left(x y^{2}\right)+\frac{1}{1+y^{2}}\right\rangle=\langle P(x, y), Q(x, y)\rangle \] (i) Determine si \2 answers -
5. Considerar el campo vectorial \( F \) cuya tercera componente es secante al cuadrado \[ F=x^{3} y^{4} \hat{i}+x^{4} y^{3} \hat{j}+\sec ^{2}(z) \hat{k} \] (i) Encontrar el trabajo hecho por la fuerz2 answers -
find x. y= (x-2)^2 y= 9 v= 81/2 pi
\( \underset{y=9+}{y \uparrow} \quad \underset{x=\frac{81}{2} \pi \text { am.unit s s }}{\longrightarrow} \)2 answers -
Use logarithmic differentiation to find \( y^{\prime} \). \[ y=\frac{\sqrt{6-7 x}\left(x^{2}+4\right)^{2}}{x^{2}+3 x+7} \] \[ y^{\prime}= \]2 answers -
asap
\( \begin{array}{l}\text { Find } f^{\prime}(x) \text { if } f(x)=\int_{1}^{x^{2}}(t+\sin t) d t \\ \qquad \begin{array}{l}x^{2}+\sin x^{2} \\ \int_{1}^{2 x}(t+\sin t) d t \\ \int_{1}^{x^{2}}(1+\cos t2 answers -
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valuate the triple integral \( \iiint_{E} f(x, y, z) d V \) over the solid \( E \). \[ f(x, y, z)=z, E=\left\{(x, y, z) \mid x^{2}+y^{2} \leq 9, x \geq 0, y \geq 0,0 \leq z \leq 1\right\} \]2 answers -
Evalúe la integral triple:
11. \( \iiint_{E} \frac{z}{x^{2}+z^{2}} d V \), donde \[ E=\{(x, y, z) \mid 1 \leqslant y \leqslant 4, y \leqslant z \leqslant 4,0 \leqslant x \leqslant z\} \]2 answers -
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\( \begin{array}{l}f(x, y)=\left\{\begin{array}{ll}\frac{x y\left(x^{2}-y^{2}\right)}{x^{2}+y^{2}} & \text { if }(x, y) \neq(0,0) \\ 0 & \text { if }(x, y)=(0,0)\end{array}\right. \\ f_{x x}(0,0) \\\e2 answers -
\( \begin{array}{l}\text { if } f(x, y, z)=\frac{\ln (-5 y z)}{(7 x-1)^{4}}-\frac{9 x^{3}}{y^{5} z^{2}} \\ f_{z y z}=\frac{1890 x^{3}}{y^{8} z^{2}}+\frac{2}{(7 x-1)^{4} y^{3}} \\ f_{z y z}=\frac{270 x2 answers -
1) Evalúa las siguientes integrales de línea sobre las curvas indicadas a) \( \int_{C}\langle 2 x y, x-2 y\rangle \bullet d \vec{r} \) donde \( \mathrm{C}: \boldsymbol{r}(t)=\operatorname{sen}(t) \b2 answers -
2) Calcula el trabajo realizado por cada uno de los campos vectoriales siguientes al moverse sobre la trayectoria dada, el arco se mide en metros y la fuerza en newtons. a) \( \boldsymbol{F}(x, y, z)=2 answers -
Evalúa las siguientes integrales de línea: a) \( \oint_{C} x^{2} y d x-y^{2} x d y \) donde C es la circunferencia \( x^{2}+y^{2}=1 \). Respuesta \( -\pi / 2 \). b) \( \oint_{C}(x+y) d x+x y d y \)2 answers -
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Resuelve este IVP 4(sin(t)dy/dt+(cos(t))y)=(cos(t))(sin(t))^7 para 0<t<pi y y(pi/2)=10. Encuentra y.1 answer
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Please show all work.
23-24 Find \( \nabla \cdot(\mathbf{F} \times \mathbf{G}) \) \( \begin{array}{l}\mathbf{F}(x, y, z)=y z \mathbf{i}+x z \mathbf{j}+x y \mathbf{k} \\ \mathbf{G}(x, y, z)=x y \mathbf{j}+x y z \mathbf{k}\2 answers -
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