Calculus Archive: Questions from July 27, 2023
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Calculate the iterate integral. Need help with all the questions below.
c) \( \int_{0}^{1} \int_{0}^{1}\left(x+e^{-y}\right) d x d y \) d) \( \int_{0}^{\pi / 6} \int_{0}^{\pi / 2}(\sin x+\sin y) d y d x \) e) \( \int_{1}^{3} \int_{1}^{5} \frac{\ln y}{x y} d y d x \)2 answers -
11. Find the derivative of the following function. (a) \( f(x)=\left(x^{3}-10\right) \cdot \tan (12 x) \) (b) \( f(x)=12 e^{-4 x} \cdot \cos (2023 x) \) (11) (a) \( f(x)=\left(x^{3}-10\right) \cdot2 answers -
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Find each limit. \[ f(x, y)=x^{2}-9 y \] (b) \( \lim _{\Delta y \rightarrow 0} \frac{f(x, y+\Delta y)-f(x, y)}{\Delta y} \)2 answers -
Se necesita pintar la región que esta acotada por la gráfica de la función \( f(x)=\frac{1}{x^{2}+1} \), la recta \( x=k \) y los dos ejes coordenados Un contratista menciona que la región que se2 answers -
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Find the derivative of the following functions: a. \( \quad y=\sqrt{x^{3}} \) b. \( y=x^{-4 / 7} \) c. \( y=\sin ^{2} x^{2} \) d. \( y=\left(x^{3}\right)\left(3^{x}\right) \) e. \( \quad y=\frac{x}{e^2 answers -
Solve [x y]= [1 1 -17 -1 ] [x y ], x(0) = -2, y(0) = -14
Solve \[ \begin{array}{l} {\left[\begin{array}{l} x^{\prime} \\ y^{\prime} \end{array}\right]=\left[\begin{array}{cc} 1 & 1 \\ -17 & -1 \end{array}\right]\left[\begin{array}{l} x \\ y \end{array}\righ2 answers -
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Evalúa la integral ∫sec^2t/tan^2t+3tant+2 dt la respuesta correcta es -ln|2tan(t)+4|-ln|2tan(t)+2|+c2 answers
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Find \( f_{x} \) 16) \( f(x, y)=\frac{x^{2}-y^{2}}{x^{2}+y^{2}} \) Find \( \mathbf{f}_{x} \) 14) \( f(x, y)=y \ln \left(\frac{1}{x}\right) \)2 answers -
Evaluate the following integral. cos²x dx 11 sin 1 sin x cos x dx [11 sin ³x cos ²x dx =
Evaluate the following integral. \[ \int 11 \sin ^{3} x \cos ^{2} x d x \] \[ \int 11 \sin ^{3} x \cos ^{2} x d x= \]2 answers -
(1 point) Find the Jacobian. \( \frac{\partial(x, y, z)}{\partial(s, t, u)} \), where \( x=3 t-3 s-5 u, y=2 u-(2 s+5 t), z=s+5 t+u \). \( \frac{\partial(x, y, z)}{\partial(s, t, u)}= \)2 answers -
Find the first partial derivatives of the function. \[ f(x, y, z)=x^{7} y z^{2}+2 y z \] \[ f_{x}(x, y, z)= \] \[ f_{y}(x, y, z)= \] \[ f_{z}(x, y, z)= \]2 answers -
Differentiate. (12 pts) B. c.
\( y=(2 x+1)^{5 / 2}(4 x-1)^{3 / 2} \) \( y=\frac{x^{2}-6 x}{x-2} \) \( y=(4 x-1)(3 x+1)^{4} \)2 answers -
For the given parametric equations, find the points \( (x, y) \) corresponding to the parameter values \( t=-2,-1,0,1,2 \). \[ x=3 t^{2}+3 t, \quad y=3^{t+1} \] \( t=-2 \quad(x, y)=(\quad) \) \( t=-12 answers -
Find the Jacobian of the transformation. \[ x=7 v+7 w^{2}, \quad y=2 w+2 u^{2}, \quad z=5 u+5 v^{2} \] \[ \frac{\partial(x, y, z)}{\partial(u, v, w)}= \]2 answers -
Given \( f(x, y)=4 \sqrt{7 x^{6}+5 y+x y^{5}} \) \[ \begin{array}{l} f_{x}(x, y)= \\ f_{y}(x, y)= \end{array} \]2 answers -
Given f(x, y) = -5x5 - xy² + 2y6, find fx(x, y) = fy(x, y) =
Given \( f(x, y)=-5 x^{5}-x y^{2}+2 y^{6} \) \[ \begin{array}{l} f_{x}(x, y)= \\ f_{y}(x, y)= \end{array} \]2 answers -
Una caja rectangular apoyada sobre el suelo (plano xy con un vértice en el origen) y el vértice opuesto en el plano \( 6 x+4 y+3 z=24 \). La empresa "FEDEX" te contrata para calcular el máximo volu2 answers -
3. Esta empresa de metal te pide calcular la masa de la lámina correspondiente al primer cuadrante de la ecuación \( x^{2}+y^{2}=4 \), si la densidad de la lámina en \( (x, y) \) es \( \rho(x, y)=62 answers -
4. Requieres calcular el área de la región comprendida entre la función \( y=4 x-x^{2} \) y el eje ' \( x \) ', por encima de la ecuación \( y=-3 x+6 \), dado en kilómetros para la construcción2 answers -
5. Se pide además calcular el volumen de otra presa en el Zapotillo acotada por la superficie \( f(x, y)= \) \( e^{-x^{2}} \) y los planos \( y=0, x=1, x=y \) en kilómetros. 6. Cambia en orden de in2 answers -
\( \begin{array}{l}\text { Given } f(x, y)=4 x^{6}-2 x y^{3}+3 y^{4} \\ f_{x x}(x, y)= \\ f_{x y}(x, y)= \\ f_{y y}(x, y)= \\ f_{y x}(x, y)=\end{array} \)2 answers -
Consider the function. \[ f(x, y)=y+x e^{y} \] (a) Find \( \int_{0}^{4} f(x, y) d x \). (b) Find \( \int_{0}^{1} f(x, y) d y \).2 answers