Evaluate 1 x² + y² + z² E between the spheres x² + y² + x² + y² + z² ///₂ = dV, where E lies ² = 4 and = 16 in the first octant.

Q: 16. Calculate ]] (V × F) · în dS, where F = (y, −x, e²²) and S is the part of paraboloid z = 3x² +…

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Q: O surlace U(X,y) = xy? 6. Transform the three-dimensional Laplacian Vu = u,, + Uy + u, to spher-…

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Q: Q3// B Verify that dv3p'sin Ddpd@d owhen using spherical coordinate

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Q: Q.1) Use the polar integral to evaluate /1-(r-1)² r+y dydr 1² + y?

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Q: 5. Consider a parabolic solar panel which lies in the part of z = x2 + y? below the plane z = 1,…

A: Solution...

Q: Find the length of the parametric x = e*, y = e=t, z = /2t, where 0 <t<1. ||

A: Given: x=et, y=e-t, z=2t  where 0≤t≤1

Q: Use Stokes' Theorem to compute 1 z? dx + (ry) dy + 2020 dz, where C is the triangle with vertices at…

A: Given I=∮C12x2+xydy+2020dz where C is the triangle with vertices at 1,0,0 , 0,2,0 , 0,0,2 traversed…

Q: Let 0 € [0, 27). Let A = cos 0 - sin sin 0 cos 0 ve R². (1) What is the length of Av, in terms of…

A: We use the given information.

Q: 2. Let r>o and Fo tina20 And use polar coordinates KZQ and use polar coordiinates (8,7) >(0,0)

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Q: baphress -4i in esponenial form reio the Qunge OLOC2TI in

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Q: Find a parameterization for the quarter sphere x² + y² + z² = a² where z > 0 and x > 0.

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Q: Find the first and second fundamental form of x(u,v)=(e(u-v)/2 cos(u+v)/2, e(u-v)/2…

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Q: Find the coordinates of L" if ALMN with L(1, 2), M(-2, 6), and N(-1, 5) is rotated 90° about the…

A: Given: L(1,2) , M(-2,6), and N(-1,5)

Q: 37.Calculate the value of r such that the line x + 2 y + z = 0 is a center-line of the conic section…

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Q: (1) Find the area of the curved surface of the upper half of the sphere x2 + y² + z² = a²(a > 0) on…

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Q: (Compute Sc (-3y+ony Sin(3))dxt (5x²-(ye)du Where C is a Simple Clased cUne in the plane oriented…

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Q: A hole is drilled through the center of a sphere x² + y² + z? = R,², leaving a ring-shape solid. If…

A: given sphere x2+y2+z2=R2s and a drill of cylinderical shape x2+y2=R2d use polar coordinate to…

Q: 1. a) Evaluate I = S S Sp(x² +y² – 1) dV, where E lies between the spheres a2 + y? + 22 = 9 and a? +…

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Q: Cvaluate AP G is a solid in the first octant bounded by the plane y+ z = 2 and the urface y = 1 -…

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Q: b. Let g(x, y) = (2xy +e² − 3)i + (x² − y² +sin y)j. Calculate g(r) dr where C' is the ellipse 4x²…

A: Since there are two questions, therefore find the solution of the first question.