Calculus Archive: Questions from April 06, 2023
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solve highlighted question with steps only the highlighed questions with steps
(a) Evaluate \( f(1,1,1) \). (b) Find and describe the domain of \( f \). 12. Let \( g(x, y, z)=x^{3} y^{2} z \sqrt{10-x-y-z} \). (a) Evaluate \( g(1,2,3) \) (b) Find and describe the domain of \( g \2 answers -
Find \( y \) ' by implicit differentiation. Match the equations defining y implictif with the ethes ebery the exremsior \[ \begin{array}{l} \text { 1. } 6 x \sin y+6 \cos 2 y=2 \cos y \\ \text { 2. }2 answers -
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1-54 Use the guidelines of this section to sketch the curve. 31. \( y=\sqrt[3]{x^{2}-1} \) 32. \( y=\sqrt[3]{x^{3}+1} \) 1. \( y=x^{3}+3 x^{2} \) 2. \( y=2 x^{3}-12 x^{2}+18 x \) 33. \( y=\sin ^{3} x0 answers -
Solve the initial-value problem \( x y^{\prime}=y+x^{2} \sin x, y\left(\frac{\pi}{4}\right)=0 \). Answer: \( y(x)= \)2 answers -
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Problem 6.4 Find the GS of \[ y^{\prime \prime \prime}-y^{\prime \prime}+y^{\prime}-y=1+\sin x+\sin 2 x+e^{x}+e^{-x} \]2 answers -
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Let \( F(x, y, z)=\left(7 x z^{2}, 0,-3 x y^{3} z\right) \) be a vector field and \( f(x, y, z)=x^{3} y^{2} z \). \[ \begin{array}{l} \nabla f=( \\ \nabla \times F= \\ F \times \nabla f=( \\ F \cdot \2 answers -
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III. Determine la derivada direccional de la función en dirección de PQ \( f(x, y)=x^{2}+3 y^{2} \) donde \( P(1,1) \) y \( Q(4,5) \). IV.Determine el gradiente de la función y la dirección de má2 answers -
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only answer the markes Q only answer the mared Q thansk answer the marked qustions the pink marking
14. \( f(x, y)=\sqrt[4]{x}-3 y \) 15. \( f(x, y)=\ln \left(9-x^{2}-9 y^{2}\right) \) 16. \( f(x, y)=\sqrt{x^{2}+y^{2}-4} \) 17. \( g(x, y)=\frac{x-y}{x+y} \) 18. \( g(x, y)=\frac{\ln (2-x)}{1-x^{2}-y^0 answers -
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Compute the gradient vector fields of the following functions: \[ \begin{array}{ll} \text { A. } f(x, y)=5 x^{2}+9 y^{2} & \\ \nabla f(x, y)= & \text { i+ } \end{array} \] \[ \begin{array}{ll} \text {2 answers -
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Express the solution of the given initial value problem in terms of a convolution integral. \[ y^{\prime \prime}+6 y^{\prime}+25 y=\sin \alpha t, \quad y(0)=0, \quad y^{\prime}(0)=0 \] \[ \begin{array2 answers -
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\( \begin{array}{l}y=10 e^{4 x}-2 x^{2}+7 \\ y=\left(x^{2}+3 x-5\right)^{3} \\ y=x^{2}(x+5)^{3} \\ y=\frac{x^{2}}{x+4}\end{array} \)2 answers -
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