Identify and sketch the following set in cylindrical coordinates. {(r,0,z): 0

Q: Which of the following is the cylindrical coordinates of (–1, /3, –2)? O a. (2, 5,–2) O b. (4, 5,…

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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 the…

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Q: Let D be the unit disk: x + y² < 1. Evaluate I| 7exp(x² + y²) dx dy by making a change of variables…

A: Given:The integral

Q: The area of the plane z = 2x + 1 above the disk of radius 1 centered at the origin is (а) 4л. (b)…

A: As we know, z=fx,y defines a surface in xyz-space.  Formula for the surface area of the surface…

Q: Describe the surface S, defined by 0 ≤ x ≤ R, 0 ≤ y ≤ x and z = R, using spherical coordinates r, θ…

A: the surface S, defined by 0 ≤ x ≤ R, 0 ≤ y ≤ x and z = R, using spherical coordinates r, θ and φ

Q: Evaluate F · dī where C F = , and C is the circle of radius 3 centered at the origin parametrized…

A: To find  ∫CF→.dr→ where c is circle of radius 3 centered  at origin parametrized in counterclockwise…

Q: Which of the following surfaces cannot be described by setting a spherical variable equal to a…

A: Given,ρ=k , ϕ= k , θ=k To check which one of the given surfaces cannot be described in the above…

Q: Use Stokes' theorem to evaluate (ry – y) i – In zj+ (r+r²) k) - dr, where C is the intersection…

A: Let F be a vector field and C be the boundary of the surface S. The Stoke's theorem states that…

Q: Let E be the ball of radius 5 centered on the origin from which the cylinder about the z-axis of…

A: We can solve this using definition of sphere cylinder and parametrization

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: Identify the restrictions on r, 0, and z created by the graph (in cylindrical coordinates) shown. -4…

A: Here we have to identify the restriction on r, theta and z from the figure.

Q: describe the given set in spherical coordinates  x2 + y2 + z2 ≤ 1, x = y, x ≥ 0, y ≥ 0

A: x2+y2+z2≤1,  x=y,  x≥0,  y≥0. Consider, x2+y2+z2≤1⇒ρ2≤1              ∵ρ=x2+y2+z2⇒0≤ρ≤1 &amp;…

Q: find an equation of the form r = f (θ , z) in cylindrical coordinates for the following surfaces.…

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Q: Convert the following point from cylindrical to rectangular coordinates: 10, (x, y, z) = Usage: To…

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Q: Find the center of mass, the moment of inertia about the coordinate axes, and the polar moment of…

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Q: describe the given set in spherical coordinates  y2 + z2 ≤ 4, x = 0

A: y2+z2≤4,  x=0. Now consider, y2+z2≤4⇒x2+y2+z2≤4+x2⇒x2+y2+z2≤4             ∵x=0⇒ρ2≤4⇒0≤ρ≤2 Now since…

Q: 6a 7 - 8a3 (a >0) I cacose ava2-r2 Jo Jo z"dzdrd0 =

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Q: Let M = { (x; y; z)TER3: x2 + y2 < 5,0 <z <2,x<ys0}R3. By which one Expression is a parameterization…

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Q: Identify and sketch the following set in cylindrical coordinates. {(r,0,z): 3r szs 3}

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Q: In changing variables to cylindrical coordinates, the dV in I| f(x, y, z) dV becomes pdz dr do. O…

A: The objective here is to check if changing the variables to cylindrical coordinates the dV in…

Q: find an equation of the form r = f (θ , z) in cylindrical coordinates for the following surfaces. z…

A: To find an equation of the form r=fθ,z in cylindrical coordinates of given surfaces: z=x+y Solution:…

Q: Exercise 2 Use spherical coordinates to evaluate [[[(9-x - y³) dV , where E is the solid hemisphere…

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Q: describe the given set in spherical coordinates x2 + y2+ z 2 ≤ 1

A: Given: x2+y2+z2≤1 Spherical coordinates: x,y,z→ρ,θ,ϕ ρ2=x2+y2+z2

Q: find an equation of the form r = f (θ , z) in cylindrical coordinates for the following surfaces.…

A: Given: The surface, x2+y2+z2=4.

Q: YouTrylt 5 Sketch the solids described by the given inequalities in cylindrical coordinates. 0 sr…

A: Answer

Q: Find an equation of the form r = f (θ, z) in cylindrical coordinates for the following surfaces. z =…

A: We have to convert the following surface into the equation of the form r = f (θ, z) in cylindrical…

Q: H=pz coup ap te'sing a4 tp'ar At point (1, ,0)

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Q: Use cylindrical or spherical coordinates, whichever seems more appropriate, to evaluate lies above…

A: Solution: ∬∫E z dV z = x2 +y2  ,     z =4

Q: Use spherical coordinates. SI. Evaluate Vx2 + y2 + z2 dV, where E lies above the cone z = Vx2 + y2…

A: The spherical coordinate system is a polar coordinate system used to translate cartesian plane to…

Q: Let G be the solid in the first octant bounded by the sphere 2x? + 2y? + 2z? = 32 and the coordinate…

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Q: describe the given set in spherical coordinates x2 + y2 + z2 = 1, x ≥ 0, y ≥ 0, z ≥ 0

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Q: Describe the set of all points P = (x, y,z) satisfying x^2 + y^2 ≤ 4 in both cylindrical and…

A: Given,        x2+y2≤4

Q: (a) Express the following points in cylindrical and spherical coordinates: (i) P(l, -4, -3); and…

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Q: Which one of the following accurately describes the set {(r, 0, 2) |r = 5 } %3D in cylindrical…

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Q: Which of the following is the cylindrical coordinates of (-1, –/3,2)? O a. (4, 품, 2) O b. (2, 플, 2)…

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Q: Let G be the solid in the first octant bounded by the sphere 2x? + 2y? + 2z? and the coordinate…

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Q: Convert the following point from cylindrical to rectangular coordinates: (* ). 11a 6, (x, Y, z) =…

A: The given point in cylindrical coordinates are   6,11π6,9. We know that if cylindrical coordinates…

Q: 2. Let W be the portion below the plane z = centered at the origin in R3. Give a domain for…

A: We will use relation between cartesian and spherical co ordinate to find domain of W

Q: The r in cylindrical coordinates must be positive or zero. O True O False

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Q: Find D at P(0,0,8) due to a disk of surface charge 15nC/m2, p< 5 m lies on the z=0 plane

A: To find the electric field due to a charged disk. The surface charge of the disk is, σ=15…

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: Which of the following is the cylindrical coordinates of (-1, y/3, –2)? O a. (2, 플, -2) O b. (2, 폭,…

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Q: sketch the region described by the following cylindricalcoordinates in three-dimensional space. 0 ……

A: The given region is  0≤r≤3-π2≤θ≤π20≤z≤rcosθ   Sketch this region in cylindrical coordinates as shown…

Q: Find the average x-coordinate of a point on the half-torus with the following parametrization (drawn…

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Q: Use cylindrical coordinates to find the vol- ume of the solid that lies within both the 2 cylinder…

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Q: 2. Use Stokes' Theorem to evaluate ſ. V × F·n dS where F(x, y, z) = and C is the part of the sphere…

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Q: Use the polar coordinates to evaluate volumes : 1 2) Below z = 1– x² – y² inside x? + y2 above the…

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Q: Let C be the curve in the plane with parametrization r(t) = cos ti+ sin tj for t e [0, 4T]. Compute…

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Q: In cylindrical coordinates, the set {(r, 0, z): 0<r< 1, 0<0 <T, -1 <z < 1} is (a) a full right…

A: In the given cylindrical coordinates, r,θ,z Radius of the cylinder lies between 0 to 1. r=0≤r≤1r=1…