A) dS = v36u4 + 16u² + 36v² dA B) dS = V16u4 + 36u² + 36v² dA C) dS = v6u? – 4u – 6v dA D) dS = v36ut + 36u? + 16v² dA

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

A:

Q: (4) Let S be the surface parametrized by I= r cose y =r sin e 2= 30 where and Evaluate the integral…

A:

Q: A hole is drilled through the center of a sphere x² + y² + z² = R,², leaving a ring-shape solid. If…

A: A per your request , (b) The equation of sphere is given as , x2+y2+z2=Rs2 and Radius of drill=Rd…

Q: A hole is drilled through the center of a sphere x² + y² + z² = R,², leaving a ring-shape solid. If…

A: The radius of the sphere is 'Rs' and radius of cylindrical driller is 'Rd'. When the cylindrical…

Q: A large conducting cone ( 0=30° )is placed on a conducting plane with a tiny gap separating it from…

A: A large conducting cone is placed on a conducting plane with a tiny gap separating it from the plane…

Q: 1: Describe the solid bounded by the sphere ² +y² + z² = 9 and the pla 2 over the xy-plane using %3D…

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Q: (5) Use Stokes' Theorem to find the line integral |(* + 2y°)i + (y + z°) +(= + 2r*)k) • dř where C…

A:

Q: The double integral I S Vx2+ y dydx in polar coordintes is:

A: Given: To explain the correct option of the given statement as follows,

Q: 1 Find the area of the surface obtained by rotating the curve y = In(1 – x²), 0 < x <. about the

A:

Q: Consider the surface S shown in the gure and whose parameterization is given by: r(u, v) = (sin v,…

A: Consider the surface S shown in the gure and whose parameterization isgiven by: r(u, v) = (sin v, u…

Q: 1. Find by integration the area of the surface of revolution generated by revolving the loop about…

A:

Q: Asap Find the characteristic strips of the equation ap+yq-pq = 0 and obtain the equation of the…

A:

Q: 2. a. Calculate the surface integral of /(x.y,z) = obtained by parametric equation: over the full…

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Q: 14. (a) Give a parametrization for the intersection of y = x² and z = e". (b) Set up an integral…

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Q: As shown in the picture at right, a solid is bounded below by the xy-plane, above by the sphere x² +…

A:

Q: 2. Use Stokes theorem to evaluate fs da. a) a = x2 sin z da + y? dy + ry dz, S is the part of the…

A: As per our guidelines, we are supposed to answer only one question and rest can be reposted Given:…

Q: Find the volume of a right circular cylinder of radius a = 4.00 with a paraboloid of revolution…

A:

Q: (6) Calculate the surface integral SSs F · ñdS where F = (ze", –3ze"V, xy) and S is the…

A: Given that,

Q: Consider the parametrization y: [0,47] → R, (t) = (t cos t, t sin t), of a counter-clockwise spiral…

A:

Q: A hole is drilled through the center of a sphere x?+y² + z² = R,?, leaving a ring-shape solid. If…

A:

Q: Use cylindrical coordinates to show that the volume of a sphere of radius a from which a central…

A: If a cylinder of radius b is cut from a sphere of radius a, then the volume of sphere depends on the…

Q: 4. Consider the surface given by z = x x²esin y. (a) Find the equation of the tangent plane to z =…

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Q: x = tsin (4t), y = tcos (4t), 0 ≤ t ≤ π / 2, which is the surface area integral of the body formed…

A: The volume of the body by revolving around the x-axis in the parametric form is given as So only B,…

Q: Evaluate the unoriented line integral (2æ² + y² + z²) ds along the parametric curve a : [0, 1] → R³…

A:

Q: Suppose that C is the curve of interesection between the plane z = x and the cylinder x² + y? be the…

A: Consider the given function. z=x and x2+y2=1 As, the function S be the interior of this ellipse…

Q: In exercises 13-18, compute the surface area of the surface obtained by revolving the given curve…

A: Solving part (b) as requested. Given:

Q: Consider the spherical surface E of center at C= (0,0.2) and radius 3. There are two planes parallel…

A:

Q: Compute the integral of the Gauß curvature over the surface shown in the picture. The three boundary…

A:

Q: There is a curve parametrized by x = 3t, y = 2t°, 0<t an equation for this curve in terms of ne…

A: Here we have,

Q: Use Stokes' Theorem to evaluate L* + cos x) dx + (sin y + z²) dy + x dz where C is the closed curve…

A: To Evaluate: Use Stoke's Theorem:

Q: 3. Please give clear explanations

A: The parametrization of a surface S is given by       G(u, v)=(u, v, uv) where D is u2+v2≤1.

Q: Find the volume of the solid bounded by the plane z = 0 and the paraboloid z = 9 - x2 - y2. SOLUTION…

A: Solution

Q: Here's a picture of the parametric surface r(u, v) = (u cos v, u sin v, uv) for 0 ≤ u ≤ 12,0 ≤ v ≤…

A: As per the question we are given a parametric surface r(u, v) and we have to find the surface area…

Q: u' cos u?, r? EXAMPLE 6.6.3 For a surface of revolution defined by x u sin u?, x3 = f (u'), where f…

A:

Q: # 4. Use Green's Theorem to evaluate the line integral P (y*dx +2xy° dy), where C is the positively…

A: Given integral is, ∮Cy4dx+2xy3dy

Q: u' cos u?, x? EXAMPLE 6.6.3 For a surface of revolution defined by x u' sin u?, x³ = f (u'), where f…

A:

Q: In which of the choices below is a parametrization for the tangent line to the curve of intersection…

A: “Since you have asked multiple question, we will solve the first question for you. If youwant any…

Q: Find an equation of the form r = f(0) in cylindrical coordinates for the surface 6x2 + 6y² = 13. %3D

A:

Q: Compute the surface area of the surface generated by revolving the astroid with the parametrization…

A: In this question, we find the surface of revolution by rotating the given parametric curve around…

Q: The parametric surface R (r, 0) = A = ) = r cos (i + r sin 0j + 0k, for 0 ≤ 0 ≤ 6π, 0 ≤ r ≤ 1, is a…

A: Given parametric surface  R→r,θ=rcosθi+rsinθj+θkfor 0≤θ≤6π, 0≤r≤1

Q: 4) The area of the surface generated by revolving x=y²-1, 1≤ y≤ 2 about x-axis is S=.

A:

Q: Consider the surface S which is the part of the cylinder x^2 + z^2 = 9 , whit   0 ≤ y ≤ 2; x ≥ 0; z…

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Q: Let C be the intersection curve of the paraboloid z = x2 − y2/2 with the cylinder x2 + y2 = 1,…

A:

Q: S Find the voleime of the solid generated by revolving the region baunded by the given lines Cnd…

A: Hint: Try Disk Method to find the volume.

Q: (10) Sketch the solid bounded by z = x2 + y? and z 4- x2 - y². Use cylindrical coordinates to find…

A: Given ∫∫∫Dx2+y2dVand solid bounded by z=x2+y2 and z=4-x2-y2

Q: dr 2 +r² dt, 2 L = dz' (dt. dt, x = rcos(0) y = rsen(0).

A: Given a parametric curve x=rcosθ, y=rsinθ, z=z(t)  for a&lt;t&lt;b To show…

Q: Let G(x, y, z)= (1+9xy)² and consider a surface S given by the parametrizatio Osus2,0svs2. Then the…

A: Here we have,    and surface S by the parametrization We have to find,

Q: 17. Let T be the solid bounded below by the half-cone z = Vr2 + y? and above by the spherical…

A: Consider T be the solid bounded below by the half cone z=x2+y2 and above by the sphere x2+y2+z2=1.…

Q: 3. Find the area of the surface generated by revolving the curve about the given axis: x = g(y) =…

A: ds= sqrt(1+(dx/dy)^2)

Q: The area of the surface obtained by rotating the curve y = et +e asxsb, about the x-axis is 1/2 e2 +…

A: Find the surface area rotating the curve about x axis