Calculus Archive: Questions from May 06, 2023
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4. (a) Find \( f_{x y}(0,3) \) and \( f_{y y}(0,3) \) if \( f(x, y)=\sin x y+x e^{y} \). (b) If \( w(x, y)=\tan \left(x^{2}+y^{2}\right)+x \sqrt{y} \), show that \( w_{x y}=w_{y x} \).2 answers -
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[valor 20 pts] Resuelva la ecuación diferencial que se muestra usando el modelo de "Exactas" \[ \left(3 x y+y^{2}\right)+\left(x^{2}+x y\right) \frac{d y}{d x}=0 \]2 answers -
[valor 10pts] Resuelva la ecuación diferencial que se muestra usando el modelo de sustitución "Homogéneas con \( v=y / x \) " \[ \frac{d y}{d x}=\frac{3 y^{2}+x y}{x^{2}} \]2 answers -
[valor 10pts] Resuelva la ecuación diferencial que se muestra usando la sustitución de Bernoulli \[ y^{\prime}+\frac{4}{x} y=x^{3} y^{2} \]2 answers -
[valor 10pts] Resuelva la ecuación diferencial que se muestra usando el modelo de sustitución con \( u=A x+B y+C \) \[ \frac{d y}{d x}=(-x+y+1)^{2}+1 \]2 answers -
question e and c. show all steps
3. Determine \( y^{\prime} \) for each of the following: a. \( y=\tan (\sin x) \) d. \( y=(\tan x+\cos x)^{2} \) b. \( y=\left[\tan \left(x^{2}-1\right)\right]^{-2} \) e. \( y=\sin ^{3} x \tan x \) c.2 answers -
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Find the Jacobian of the x = 2v + 2w², a(x, y, z) ò(u, v, w) transformation. y = 8w + 8u², y = 8w+8u², z = 4u + 4v²
Find the Jacobian of the transformation. \[ x=2 v+2 w^{2}, \quad y=8 w+8 u^{2}, \quad z=4 u+4 v^{2} \] \[ \frac{\partial(x, y, z)}{\partial(u, v, w)}= \]2 answers -
20 III. y dV, where E = {(x, y, z) | 0≤x≤ 3,0 ≤ y ≤ x, x - y ≤ z ≤ x + y} Evaluate the triple integral.
Evaluate the triple integral. \[ \iiint_{E} y d V, \text { where } E=\{(x, y, z) \mid 0 \leq x \leq 3,0 \leq y \leq x, x-y \leq z \leq x+y\} \]2 answers -
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Using the inverse function Theorem, show that the derivative of the tenction \[ y=\log _{a} x \quad \rightarrow \quad y^{\prime}=\frac{1}{x \ln (a)} \] Teorema para Funciones Inversas Sea \( f \) una2 answers -
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