3) Prove thet the xy-plane with constant curva tue k= urve In is o circle of radious

Q: By using Green's theorem evaluate £ (Ary – y") dr + (** + 3ry) dy where C is a closed curve starting…

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Q: Compute the line integral (Баллов: 2) Jo ds, Cis the right half of circle x2 + y 16 (counter…

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Q: 2. Find the coordinate of the points on the cardioid r=1- cose at which there is a horizontal…

A: We are given the polar curve: r = 1- cosθ use formula:         x=r cosθy=r sinθ then,  dxdθ=-sinθ+2…

Q: 6. Where does the tangent line to r = at the point (1, 0, 1) intersect the y-z plane.

A: Given:

Q: The value of the triple integral 6zdV where E is the upper half E of the sphere of x² + y? + z? = 1…

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Q: Find the DE of tge familiy of plane curves described and sketch some of its members 1. tanx-2x3y=c

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Q: Evaluate the line integral xdy- xydx over the closed path C where Cis the circle C

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Q: Use Green's Theorem to evaluate pxcosydx – ysinxdy, where the curve C is the square with 0), (TT,…

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Q: Suppose surface #1 is defined by o =45° , 0 <ps9, 0 < z< 6 and surface #2 is defined by 0 =56.3° The…

A: given:

Q: Set up the line integral ∫c x2z ds, where c is the line segment from (1, 6, -1) to (- 4, 1, 5). (No…

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Q: 1) The maximum distance from the origin of the xy plane to the circle described by (x – 12)? + (y –…

A: given equation of circlex-122+y-62=16 As per our guideline we supposed to answer only first question…

Q: 4. Show that the set of points (z, w) e C with w2 = sin z is naturally a Riemann surface. %3D

A: Let, S=z,w∈ℂ2|w2=sinz be the set in equation. The multivalued analytic function fz=sinz can be…

Q: 4 Find the curvature k of the plane curve y = x +- at x = 1. K =

A: Given curve is , y= x + 4x  at x=1

Q: Let C be the curve which is the union of two line segments, the first going from (0, 0) to (4, 3)…

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Q: If C is the line segment which begins at (-2, 1) and ends at (2, 4), evaluate the line integral: et…

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Q: Consider the inmplicitly defined curve xy +3x2 4. %3D O Verify that the point (1, 1) is on the…

A: Consider, the implicitely defined curve                          xy2+3x2=4 We have to verify the…

Q: Let C be the positively oriented circle x² + y² = 1. Use Green's Theorem to evaluate the line…

A: Greens theorem states that "for closed curve C enclosed a region R then the line integral along the…

Q: 8. Find a plane curve a(s) endowed with a unit-speed prametrization by S E (-∞, 0) such that its…

A: Question: Find a plane curve αs endowed with a unit-speed parametrization by s∈-∞,∞ such that its…

Q: 1. A such that the difference in distances between (x, y) and two fixed points (called is the set of…

A: A___ is the set of points (x, y) in a plane such that the difference in distances between (x, y) and…

Q: 7 Prove : id Is perpendicular line to ra duic at its outer end point ,then t ang ent to the cirde is

A:

Q: Verify Green's Theorem in the plane for F = -3y³i+ (3x3 + cos y)ĵ where C is the circle x² + y² =…

A: In this we have to verify green theorem.

Q: 1. Compute SF · dr where F(x, y) = (y²,–x²) and C is the part of th parabola u = 12 from (-1 1) to…

A: First take dot product of f and dr Then put value of y in terms of x Integrate and raise limit of…

Q: # 4. Evaluate the line integral | (x +2x²y) ds, where C is the upper half of the unit circle x2 + y2…

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Q: Calculate both sides of Green's Theorem when F = [-x²y, xy²] and y positively oriented circle x2 +…

A: According to the given information it is required to calculate both sides of the Green’s theorem.…

Q: The sphere x² + y² +z² = 100 has the center (0,0,0) and a radius of length 50. Select one: True…

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Q: Compute (ax + by² + cz) dS over the sphere x +y +z² = 1.

A:

Q: Let C be the line segment from point (0, 1, 1) to point (2, 2, 3). Evaluate line integral yds. C

A: To evaluate the line integral

Q: 4) Find the families of lines of curvature of the surface : =+ y² .

A: Given: z=x2+y2

Q: Suppose a point X lies in the exterior of a disk, and suppose that two lines are drawn from X…

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Q: 56 Consider points P and Q in the x-y plane, with P = (1,0) and Q = (0,1). The line integral 2|(xdx…

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Q: 4 6 Let y = 7 2 40 Compute the distance d from y to the plane in IR spanned by ui and uz d =

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Q: consider surface s with parami Glusv) = cu vo uv) Compute Pa, 7 Nas Tu, Tv o of s olso compute the…

A: Given surface is, G(u,v)=(u,v,uv)

Q: By using Green's theorem evaluate £ (Ary – y) dr + (** + 3ry) dy where C is a closed curve starting…

A: Green's theorem in a plane: If D is a region inclosed by a closed curve C then ∮C u dx+v dy=∫∫D…

Q: Let C be the curve of intersection of the parabolic cylinder x = 2y, and the surface 3z = xy. Find…

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Q: Let C be the curve of intersection of length of C from the origin to the poi

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Q: 5 Find the valume of the Sotids abtaind by-revelving the Yegion in the firstquadrand boundby the…

A: Sketch the graph and find the region. Using shell method, volume is evaluated.

Q: Sketch the reglon enclosed by the given curves. Dedde whether to iIntegrate with respect to or y.…

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Q: (1) Compute where Cis the couater dockwise oriented boundary of upper half unit disc D.

A: It is given that, ∮Cy2dx+3xydy here C is counter clockwise oriented upper half disc D.   Here,…

Q: 4) Find the families of lines of curvature of the surface :=r+y

A: The answer is given in handwritten format --

Q: Evaluate the line integral x²z ds, where C is the line segment from (0,6, 2) to (8, 5, 1).

A:

Q: Evaluate [[[ =*dxcydz over the sphere x +y² +=² =1.

A: to find:- to evaluate the given integral.

Q: If o is the sphere of radius 2 centered at the origin, then (x² + y² + z³) d$ =

A: Given the sphere

Q: Let C be the positively oriented circle x² + y² = 1. Use Green's Theorem to evaluate the line…

A: Greens theorem

Q: Evaluate the line integral ∫Cx2yds along the segment of the line y=x from the origin up to the point…

A:

Q: - Show that the distance r from the origin O to the point P(Coshu,Sinhu) - on the hyperbola x-y 1 is…

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Q: Obtain the dirfferential equation of the family of plain curves given 1. All circles passing…

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Q: Let C be the curve which is the union of two line segments, the first going from (0, 0) to (1, 4)…

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Q: 10. Find a tangent plane to z² – x² +y² = 1 at (7, –5, 5).

A: To find a tangent plane to the given curve at the point (7,-5,5)

Q: Find the points on the surface xy – z2 = 1 that are closed to the origin.

A: Given surface is xy-z2=1. let xy-z2-1=0⇒z2-xy+1=0 Now distance from origin is…

Q: 7. Find the area of the portion of the plane z = 2y that lies directly above the circle x +(y-1)² =1…

A: we have to find area of the portion of plane .and coverting the problem in polar coordinate makes it…