Calculus Archive: Questions from July 20, 2023
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2.) Use Stoke's Theorem to evaluate \( \int_{\mathrm{C}} \vec{F} \cdot d \vec{r} \). \[ \begin{array}{l} \vec{F}(x, y, x)=\left\langle 3 z-\sin x, x+e^{y}, y-\cos z\right\rangle \\ \mathrm{S}: z=1-x^{2 answers -
13.) Evaluate \( \int_{C} \vec{F} \cdot d \vec{r} \). \[ \vec{F}(x, y, z)=x y \vec{\imath}+x z \vec{\jmath}+y z \vec{k} \] \( \mathrm{C}: r(t)=t \vec{\imath}+t^{2} \vec{\jmath}+2 t \vec{k}, 0 \leq t \2 answers -
Solve using the Laplace Transform. \[ y^{\prime \prime}-5 y^{\prime}+6 y=6\left(u_{2}(t)-u_{5}(t)\right) \quad y(0)=y^{\prime}(0)=0 \]2 answers -
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Find the Jacobian of the transformation. \[ x=-u^{2} v^{3}, y=u^{3} / v^{4} \] \[ \frac{\partial(x, y)}{\partial(u, v)}= \]2 answers -
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Usa el cálculo para encontrar el área A del triángulo con los vértices dados. (0, 0), (4, 5), (2, 8)0 answers
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Evalúa la integral triple ∭ E x dV donde E es el sólido acotado por el paraboloide x=3y^2+3z^2 y x=32 answers
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The volume of water that a spherical tank can hold is given by: Where: V=volume in m3 H=depth of the water in the tank in metres R= radius of the tank in metres if R =3 m At what depth should the ta
8. El volumen de agua que puede almacenar un tanque esférico viene dado por: \[ V=\pi h^{2} \cdot \frac{[3 R-h]}{3} \] Donde \( V= \) volumen en \( \mathrm{m}^{3}, h= \) profundidad del agua en el ta2 answers -
18. \( \int_{0}^{\pi / 3} \frac{\sin \theta+\sin \theta \tan ^{2} \theta}{\sec ^{2} \theta} d \theta \)2 answers -
1. Resuelve las siguientes integrales (5 puntos por integral, total 20 puntos) 1.1 \[ \int \frac{y^{2}}{(y-6)} d y \] 1.2 \[ \int \cot ^{3} \frac{x}{3} d x \] 1.3 1.5 \[ \int \frac{d x}{x \sqrt{x^{2}+2 answers -
Check that the following EDO is homogeneous and solve it.
4. Compruebe que la siguiente EDO es homogénea y resuélvela (10 puntos). \[ y^{\prime}=\frac{3 y-4 x}{2 y-3 x} \] 5. Compruebe que la siguiente EDO es exacta y resuélvela (10 puntos).2 answers -
Check that the following EDO is homogeneous and solve it.
4. Compruebe que la siguiente EDO es homogénea y resuélvela (10 puntos). \[ y^{\prime}=\frac{3 y-4 x}{2 y-3 x} \] 5. Compruebe que la siguiente EDO es exacta y resuélvela (10 puntos).2 answers -
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