Calculus Archive: Questions from July 26, 2023
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Find a formula for the derivative of the following functions. 3. \( y=3 e^{10 x}+4 x^{4} \) 4. \( f(x)=4 e^{2 x^{2}-x} \) 5. \( y=\ln \left(4 x^{3}\right)+e^{5 x} \) 6. \( y=\ln \left(3 x^{2}-5 x\righ2 answers -
Calcula el volumen bajo el plano \( 2 x+3 y+z=6 \) y sobre la región determinada por \( x=0, x=\frac{3}{2}, y=0, y=\frac{1}{2} \).2 answers -
Consideremos una tubería rectangular sobre la cual circula agua, coloquemos un sistema coordenado \( x y \) sobre una sección transversal de la tubería como se muestra en la figura, supongamos que2 answers -
Obtén el área de la región encerrada por las gráficas \( y=x^{2}+1 \) y \( y=x+1 \) mediante integral doble. Ayuda: En una integral doble, si la función \( z=f(x, y)=1 \) entonces se tiene lo sig2 answers -
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Simplify the algebraic expression. \[ \frac{x^{2}+2 x y+y^{2}}{\frac{x}{y}-\frac{y}{x}} \] \[ \frac{x^{2}+2 x y+y^{2}}{\frac{x}{y}-\frac{y}{x}}= \]2 answers -
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¿En qué punto de la curva x = 6t 2 + 8, y = t 3 − 3 la recta tangente tiene pendiente 1/2 ? (x, y) =2 answers
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calculate the Differentiate :
10) Differentiate: a) \( y=3 x^{2} \sec x \) b) \( \quad y=\frac{1+\cos x}{1-\cos x} \) c) \( y=\pi^{2}-\sqrt{3 x+1}+\left(x^{2}-1\right)^{3} \)2 answers -
9) Selecciona la función que corresponde al siguiente gráfico y justifica claramente por qué lo seleccionaste. a) \( f(x)=x^{4}-8 x^{3}+15 x^{2} \) b) \( f(x)=x^{4}+2 x^{3}-15 x^{2} \) c) \( f(x)=x2 answers -
ayúdeme por favor lo quiero para hahora
Calcular \[ \begin{array}{l} \iint(x y) d x d y ; R=[-1 ; 0] x[1 ; 2] \\ \iint(2 x-y) d x d y ; R=[0 ; 1] x[0 ; 1] \\ \iint\left(2 x+y^{2}\right) d x d y ; R=[0 ; 1] x[0 ; 2] \\ \iint\left(6 x^{2} y-20 answers -
Find the gradient vector field of f. f(x, y) = tan(2x − 4y) ∇f(x, y) =
Find the gradient vector field of \( f \). \[ \begin{array}{l} \quad f(x, y)=\tan (2 x-4 y) \\ \nabla f(x, y)= \end{array} \]2 answers -
Find y' and y". y' = y" = y = 1 Dafa 7 In(7x) x7 9 7 + In (7x) 8 X م٪۰ (7 ln 7x-1) X
Find \( y^{\prime} \) and \( y^{\prime \prime} \). \[ y=\frac{\ln (7 x)}{x^{7}} \] \[ \begin{array}{l} y^{\prime}=\frac{1}{x^{8}}-7 \frac{\ln (7 x)}{x^{8}} \\ y^{\prime \prime}=-\frac{7}{x^{9}+\frac{82 answers -
Solve for y. y' = 9x + xy; y = -1 when x = 0 y=
Solve for \( y \). \[ y^{\prime}=9 x+x y ; y=-1 \text { when } x=0 \] \[ y= \]2 answers -
Find the partial derivatives of the function \[ f(x, y)=x y e^{9 y} \] \[ \begin{array}{l} f_{x}(x, y)= \\ f_{y}(x, y)= \\ f_{x y}(x, y)= \\ f_{y x}(x, y)= \end{array} \]2 answers -
(10 points) If \( f(x, y, z)=x e^{3 y} \sin (9 z) \), then the gradient is \[ \begin{array}{l} \nabla f(x, y, z)= \\ \left(\mathrm{e}^{\wedge}(3 \mathrm{y}) \sin (9 \mathrm{z}), 3 \times\left(\mathrm{2 answers -
Solve. \[ \left[\begin{array}{l} x^{\prime} \\ y^{\prime} \end{array}\right]=\left[\begin{array}{cc} 4 & 2 \\ -53 & -14 \end{array}\right] \cdot\left[\begin{array}{l} x \\ y \end{array}\right], x(0)=22 answers -
Need help with question 26. show work
In Problems 25-32, find the indicated value. 25. \( f_{x}(1,3) \) if \( f(x, y)=5 x^{3} y-4 x y^{2} \) 26. \( f_{x}(4,1) \) if \( f(x, y)=x^{2} y^{2}-5 x y^{3} \) 27. \( f_{y}(1,0) \) if \( f(x, y)=32 answers -
Given f(x, y) = 4x + 2x²y¹ - 4y², find fz(x, y) = 24x5 + 4xy4 fy(x, y) = 8x²y³ - 8y 23 fxz(x, y) = fxy(x, y) = fyr (x, y) = fw(z,y) - می -
Given \( f(x, y)=4 x^{6}+2 x^{2} y^{4}-4 y^{2} \), find \[ \begin{array}{l} f_{x}(x, y)=24 x^{5}+4 x y^{4} \\ f_{y}(x, y)= \\ f_{x x}(x, y)= \\ f_{x y}(x, y)= \\ f_{y x}(x, y)= \\ f_{y y}(x, y)= \end{2 answers -
Given f(x, y) = -2x6 + 4x²y4 - 5y³, find fz(x, y) = 23 fy(x, y) = 16x²y3 - 15y² fxx(x, y) = = fxy(x, y) -12x5 -12x5 +8xy* = می ۔ < a
Given \( f(x, y)=-2 x^{6}+4 x^{2} y^{4}-5 y^{3} \), find \[ \begin{array}{l} f_{x}(x, y)=-12 x^{5}+8 x y^{4} \\ f_{y}(x, y)= \\ f_{x x}(x, y)= \\ f_{x y}(x, y)= \end{array} \]2 answers -
2. Identify the integral that it not well formed. [A] \( \int_{0}^{2} \int_{0}^{y} \int_{0}^{x} f(x, y, z) d z d x d y \) [B] \( \int_{0}^{2} \int_{0}^{x} \int_{x}^{y} f(x, y, z) d z d y d x \) [C] \(2 answers -
2. \( [-/ 1 \) Points \( ] \) Find \( y^{\prime} \). \[ y=\frac{\ln (5 x)}{4 x} \] 3. \( [-/ 1 \) Points] Find \( y^{\prime} \). \[ y=\log _{8}\left(x^{4}-2 x^{3}+1\right) \] \[ y^{\prime}= \]2 answers -
Evalua la integral inviertiendo el orden de integracion \[ \int_{0}^{1} \int_{\arcsin y}^{\pi / 2} 8 \cos x \sqrt{1+\cos ^{2} x} d x d y \]2 answers -
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