ify Stokes' theor d S is the surface

Q: Find the area of the surface generated by revolving the curve = V¤ + 3, 4 < y <7

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Q: Find the area of the surface generated by revolving the parametric curve x = t, y = 2t² (0 ≤ t ≤ 1)…

A: Given, x=t,y=t2,0≤t≤1 The area of the surface generated by revolving the parametric curve about the…

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: Under what conditions can you find the area of the surface generated by revolving a curve x = ƒ(t),…

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Q: Find the area of the surface generated by revolving the curve about the (a) x-axis and (b) y-axis.…

A: Explanation and solution is given below....

Q: 4: Show yor work. a) 1: Find the exact area of the surface obtained by rotating the curve y? +x =5,…

A: Since you have posted multiple questions i can do first question as per our company guidelines…

Q: Compute the Jacobian for the change of variables into spherical coordinates: x = p sin o cos 0, y =…

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Q: Compute the surface area of the surface generated by revolving the astroid with parametrization c(t)…

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Q: find the areas of surfaces generated by revolving the curves about the given axes

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Q: Find the exact area of the surface obtained by rotating the curve about the x-axis. y = √ 1 + ex,…

A: We need to find Surface area.

Q: Use Stokes's Theorem to evaluate f.7 X F.dŠ, where F (x, y, z) = (y +29)î – xj + x³yk and S is the…

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Q: I = y dx + (z — х) dy — ydz, Jc

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Q: Use Stokes' theorem to evaluate Ĝ - dĩ, vhere Ĝ(1, Y, 2) = (2r, y,0) and D is any closed curve.

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Q: Find the area of the surface obtained by rotating the curve }=2,3 from z = 0 to z = 1 about the…

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Q: erify Stokes Theorem for the ve lane x + y + z = 1 bounded b orientation.

A: It is given that F→=3x,2x-y,3y is a vector field on plane x+y+z=1 bounded by x=0, y=0 and z=0 with…

Q: dz + (y + z) dx dz surface of sphere

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Q: ns: Find the tangent plane to the surface of x2 + z² = y² + 9 at (1, –1,3). 3

A: Follow the procedure given below.

Q: Find an equation of the tangent plane to the given parametric surface at the specified point x = u?,…

A: x=u2 y=vu2 z=uv u=3 v=4 x1 =u2   x1 =9 y1 =vu2   y1=36 z1=uv z1 =12 we have to find the tangent…

Q: Find

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Q: Find the exact area of the surface obtained by rotating the curve about the x-axis. + 2)3/2, 3 sy s…

A: Given function is x=13y2+22 and 3≤y≤4 We have to find the exact area of the surface obtained by…

Q: (a) Find the area of the surface generated by the given curve about x-axis y = Vx , 1< x < 4

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Q: 3. Find the area of the surface generated by revolving the curve = 2/1- y (-1 < y < 0) X about the…

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Q: Surface at 0 = 30° and r = 10 is a.. Cylinder Cone Circle Plane

A: Solve

Q: Solve for the surface area of a plane curve rotated about y-axis. y = ((x^6)/12)+(1/(8x^4)), 1 ≤ x…

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Q: Verify Stokes's Theorem for F = z²î + x²j + y?k and S is the surface z² = x2 + y2, y 2 0, and 0 szs…

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Q: 2)Use Stokes' Theorem to evaluate [F.dr where E2xyi, y² j‡ 2xzk and Sis the first octant с surface…

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Q: Find the exact area of the surface obtained by rotating the curve x = (1/3)y^3, 0 &lt;= y &lt;= 1,…

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Q: Under what conditions can you find the area of the surface generatedby revolving a curve x = ƒ(t), y…

A: Given information,x=fty=gt; a≤t≤b To get the area of the surface generated by the curve about…

Q: Which type of surface does the curve x=t2, y = tsin(t), z=tcos(t) lie on?

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Q: SS curl F · dS =0 S

A: we have to prove that if a surface is closed then the surface integral of curlF .ds is 0 Here…

Q: Find the area of the surface obtained by rotating the curve about the y-axis. x=y', 0sys3

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Q: Consider the set S given by S = {(x, y, z) ER³ : 2 = 2x² - y²}, where A E R\{0} is constant.…

A: As per the question we are given a quadratic surface as : S = {(x,y,z) ∈ R3 | z =2x2 - λy2} And we…

Q: 4) Use Stokes theorem to evaluate SF.dr, where с F(x, y, z) = <.xy, yz, *x), where C is the triangle…

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Q: .† Use Stokes' theorem to show that Sc(y+2)dx+ (z +x)dy+ (x+y)dz = 0, where C is the curve of…

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Q: Verify Stokes' theorem for A = (p a, + cos o a, + a:) on the upper half-surface of the sphere x + y?…

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Q: * = -. y = 4 y = 4, 0 < t < 1 0 <t < 1

A: Given curve is x=4t−43t3 and y=4t2, 0≤t≤1. We have to find the area of the surface obtained by…

Q: Find the area of the surface generated by the given curve about y-axis x = y* , 1< y< 3

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Q: What is a unit normal to the surface xy + 2x

A: Given, the surface x2y+2xz=4    at  the point (2, -2, 3)

Q: Use Stokes's Theorem to show that 0= [[ curl(F) - dS where F(r, Y, z) = (2, 2ry, x + y) and S is the…

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Q: Please calculate the surface area of revolution obtained by rotating the following parametric curve…

A: Find the curve: y=tx=t22x=y22y2=2x, 0≤y≤1

Q: メ y= oL Xとn2

A: Given curve is y=ex , 0≤x≤ln2find the area of the surface

Q: Use Stokes' theorem to calculate , F.ds, where F = (z, x, y) and C is the boundary %3D of a triangle…

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Q: 3. Consider the surface sin (xy)+ cos (xz)+sin ( yz) =1. Find an equation for the tangent plane to…

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Q: B. Let C be the curve y = 1 – x2, 0< x < 1. If C is rotated about the y axis find the area of the…

A: our objective is to calculate the surface area.

Q: Find the area of the surface generated by revolving the curve about each given axis. x = 2t, y = 3t,…

A: TO FIND THE AREA GENERATED BY THE REVOLVING BELOW SURFACES x =2t y =3t ,   0≤t≤9 FORMULAS USED (a)…

Q: Find the area of the surface obtained by rotating the curve y=1/3 x3/2, 0≤y≤12  about the y- axis.

A: Let a rectangular strip parallel to x-axis of thickness dy be made whose tip touches the curve…

Q: Find the area of the surface generated by revolving the given curve about the y-axis. Szy 2y+1, 1<v<…

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Q: Find the exact area of the surface obtained by rotating the curve about the x-axis. y = x, 0< x< 5

A: Surface area of given curve after rotation about x axis.

Q: Use Stokes' Theorem to evaluate , (x + y )dx + (2x – 3)dy + (y + z)dz over the boundary of the…

A: First we will learn about Stokes theorem little bit. If "F1 i + F2 j + F3 k" is a differentiable…

Q: ii) Find the exact area of the surface obtained by rotating the curve y = x³ + 1 ≤ x ≤ 2, 1 3 12x 9

A: Use Area of surface  formula.