Let S be a surface described by x² + y² + 32² = 1, z ≤ 0, and let F(x, y, z) = yi-xj+zx³y²k. Prove that 1₁0x (V x F). dS = 2π

Q: √²³₁(−12xy² + 8x³y + 3)dxdy

A: LetWe have to evaluate the above integral.

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A: Given S as a quadric with equation 4x^2 - (y-3)^2 + 4z^2 = 4 Find a generating curve for S (as a…

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A: This question is about application of derivative

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A: NOTE: Refresh your page if you can't see any equations. . the first surface is so we can write…

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A: To find the parametrization of the curve defined by the intersection of the two surfaces  and ,…

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A: To graph the function: z=f(x,y) where f(x,y)=6xy-5x2-3y4+7x-6y

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A: From the equation of tangent, we can derive: z = -(7 + 5x + 4y) Hence,

Q: /Sketch the Surface Z=V9-X+y- and verify that fxg = Exx %31

A: Second order Partial Differentiation

Q: find    (a)    div(f)   (b)    curl(f) if f=x^2(vector i)+y^2(vector j+2yz(vector k)

A: Let's understand the mathematics behind the div and the curl functions. Please see the expressions…

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Q: Find an expression for a unit vector normal, no, to the surface x = (4 – cos (v)) cos (u), y = (4 –…

A: The complete solutions are given below

Q: Find a vector that is perpendicular to the surface 4e^{(z-1)}+x^{2}y=xyz at the point (−1,−2,1).

A: Given the surface :

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Q: y Consider the surface of equation z = X+Y² What is the equation for the tangent line to S at the…

A: This is a problem of vector calculus.

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