2022-03-10
Answered

This question concerns the vector fieldF = −xy2 i − x2y j + z(x2 + y2) k.(a) Calculate the divergence of F. Use the divergence theorem to show thatthe flux of F over any closed surface is equal to zero. (b) A cylinder of height h and radius R has its base in the xy-plane and itsaxis of symmetry along the z-axis, as shown in the diagram below.Calculate the flux of F over the curved portion S of the surface of thecylinder by using the result of part (a) to relate the flux of F over S tothe flux of F over the flat top surface T and the flux of F over the flatbottom surface B.

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nick1337

Answered 2022-03-22
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Equation of the line tangent to $\left\{\begin{array}{l}y={x}^{2}\\ {z}^{2}=16-y\end{array}\right.$, at the point (4,16,0) ?

a) $\left\{\begin{array}{l}4x=y\\ z=0\end{array}\right.$

b)$\left\{\begin{array}{l}x=4\\ y=16\end{array}\right.$

c)$\left\{\begin{array}{l}y-x=12\\ z=0\end{array}\right.$

d)$\left\{\begin{array}{l}x+y=20\\ z=0\end{array}\right.$

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use squeeze theorem find the following lim x,y-0,0 y^2(1-cos2x) /x^4 +y^2

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$U$ is a random variable that follows Uniform distribution with interval $(0,1).{X}_{1},...,{X}_{n}$ follows Bernoulli distribution with mean $U$. How do I find the function $f:(0,1{)}^{n}->R$ that minimizes $E\left[\right(U-f({X}_{1},...,{X}_{n}){)}^{2}\left)\right]$ ? I have no idea where to start solving. Thank you in advance.