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Calculus Archive: Questions from August 15, 2022

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  Given \( f(x, y)=-4 x^{5}-6 x y^{2}+y^{4} \) \[ f_{x x}(x, y)= \] \[ f_{x y}(x, y)= \]
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  \[ y^{\prime \prime}-2 y^{\prime}+6 y=\sin (3 t), \quad y(0)=2, y^{\prime}(0)=3 \] en find \( Y(s)=\mathcal{L}\{y(t)\} \). \[ Y(s)=\frac{3}{\left(s^{2}-2 s+6\right)\left(s^{2}+9\right)}+\frac{2 s-1}{s
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  Find \( \int_{0}^{2} f(x, y) d x \) and \( \int_{0}^{3} f(x, y) d y \) \[ f(x, y)=3 x+3 x^{2} y^{2} \] \( \int_{0}^{2} f(x, y) d x= \) \( \int_{0}^{3} f(x, y) d y= \) Calculate the iterated integral.
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• Find ∂f/∂x And ∂f/∂y. f(x,y)=(4xy-3)^2 ∂f/∂x= ∂f/∂y=
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• Find all the second-order partial derivatives of the following function. f(x,y)=x^2y^3−x^8+y^6 ∂^2f/∂x^2= ∂^2f/∂y^2= ∂^2f/∂y∂x= ∂^2f/∂x∂y=
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  Let \( J=\int \frac{x^{2}}{\left(1-x^{2}\right)^{3 / 2}} d x, 0
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  Let \( J=\int \frac{x^{2}}{\left(1-x^{2}\right)^{3 / 2}} d x, 0
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  Let \( J=\int \frac{x^{2}}{\left(1-x^{2}\right)^{3 / 2}} d x, 0
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• plz help
  \( f(x, y)=\sqrt{3 x^{2}+5 y^{2}} \) \( f_{x}(-5,5)= \)
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• plz help thanks
  Given \( f(x, y)=3 x^{3}-3 x y^{4}+2 y^{5} \) \( f_{x}(x, y)= \) \[ f_{y}(x, y)= \]
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  Let \( J=\int \frac{x^{2}}{\left(1-x^{2}\right)^{3 / 2}} d x, 0
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  Let \( J=\int \frac{x^{2}}{\left(1-x^{2}\right)^{3 / 2}} d x, 0
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  \( \mathbf{I}(\mathbf{F} \times \mathbf{G})=\nabla \times(\mathbf{F} \times \mathbf{G}) \) \( \mathbf{F}(x, y, z)=\mathbf{i}+7 x \mathbf{j}+4 y \mathbf{k} \) \( \mathbf{G}(x, y, z)=x \mathbf{i}-y \mat
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  \( \begin{aligned} \operatorname{liv}(\mathbf{F} \times \mathbf{G})=& \cdot(\mathbf{F} \times \mathbf{G}) \\ \mathbf{F}(x, y, z) &=\mathbf{i}+9 x \mathbf{j}+3 y \mathbf{k} \\ \mathbf{G}(x, y, z) &=x \
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  (5 points) Find the partial derivatives of the function \[ \begin{array}{l} f(x, y)=x y e^{1 y} \\ f_{x}(x, y)= \\ f_{y}(x, y)= \\ f_{x y}(x, y)= \\ f_{y x}(x, y)= \end{array} \]
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  Show that \( 2 y^{\prime \prime}-y^{\prime}-y=0 \) when \( y=e^{x}+e^{-\frac{x}{2}} \).
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• 8. Resolve dy/dx = y + 2xy (y > 0) at the point (x, y) = (1,1)
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  Find the partial derivatives of the function \[ f(x, y)=x y e^{-5 y} \] \[ f_{x}(x, y)= \] \( f_{y}(\lambda \) \[ f_{y x}(x, y)= \]
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  Given \( f(x, y)=-4 x^{3}+x y^{5}+6 y^{6} \) \[ f_{x}(x, y)= \] \[ f_{y}(x, y)= \]
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  If \( \mathbf{F}=\left\langle x^{7}, y^{-9}\right\rangle \) \( \operatorname{div}(\mathbf{F})(x, y)= \)
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  1) Utilice la definición de la derivada para hallar \( \frac{d y}{d x} \) para la función \( f(x)=-x^{2}+4 x+5 \).
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• Si consideramos el ciclo fundamental de la gráfica f(x) =3 cos (a) podemos observar los puntos donde se puede trazar una línea tangente horizontal, Qué podemos concluir del resultado de la derivada
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  Given \( f(x, y, z)=\sqrt{6 x^{2}+2 y^{2}+z^{2}} \) \[ f_{x}(x, y, z)= \] \[ f_{y}(x, y, z)= \] \[ f_{z}(x, y, z)= \]
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  Find \( \iint_{R} x^{2} d A \) where \( R=\left\{(x, y) \mid 4 x^{2}+9 y^{2} \leq 36\right\} \)
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  Problem 1 Differentiate (a) \( g(x)=(x+2 \sqrt{x}) e^{x} \) (c) \( G(x)=\frac{x^{2}-2}{2 x+1} \) (b) \( y=\frac{e^{*}}{1-e^{x}} \) I (d) \( y=\frac{\sqrt{x}}{2 x} \)
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