use green's theorem to evaluate ∫c 5y^3dx-5x^3dy where C is the circle x^2+y^2=4 counterclockwise

Q: consider surface S with paramirization Glusv) = cu. Vo uv) ノ surface of s areu also compute the

A: Differentiate Gu,v=u,v,uv with respect to u and v, to find Gu and Gv, and then compute Gu×Gv.…

Q: Evaluate the double integral. (5x – 7y) dA, D is bounded by the circle with center the origin and…

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Q: Does the Divergence Theorem apply to surfaces that are not closed?

A: By Stokes' theorem:

Q: 13. Find the area of the surface generated when the curve y = -, on [2,4] is rotated about the…

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Q: 3. Identify and sketch the surface given by z = 16-y²; 0 ≤ y ≤ 2; 0≤x≤ 4. in 3-space, include ALL…

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Q: The Green's Theorem allows us to replace any line integral over simple, smooth, closed curve in…

A: Yes, Green' Theorem allows us to replace any line integral over simple smooth closed curve in 3D…

Q: 2. Show that an equilateral triangle can be inscribed in the epitrochoid and that its centroid is on…

A: An equilateral triangle can be inscribed in the epitrochoid and that its centroid is onthe circle of…

Q: Sketch the Surface z./4-x* and verify that fay -lyx.

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Q: Sketch the surfaces PARABOLOIDS AND CONES z = 8 - x2 - y2

A: Consider the equation of the surface, z = 8 - x2 - y2

Q: Use Green's theorem in order to compute the line integral £ (x – 3)³ dy – y³ dx where is the circle…

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Q: Describe the transformation rules that map Circle F onto Circle F'. Translation rule: (x, y) -->…

A: We have to find dialtion

Q: Find the equation of the tangent plane to the surface y = 2x2 - z2 at the point (0, –1, –1) %3D | |

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Q: The area of the surface obtained by rotating the curve y = V9-x2, -1sxs1 about the x-axis is mit…

A: Use formula of surface area about x axis

Q: Calculate the surface area of the z=x²+y surface on the triangular region with vertices (0,0), (1,0)…

A: Let z=fx,y. Differentiate the function fx,y with respect to x and y, to obtain fxx,y and fyx,y.…

Q: Describe the transformation rules that map Circle A onto Circle B. Translation rule: (x, y) --> (x…

A: Dilation and transformation of circle

Q: Find the area of the part of the surface z = x² + 2y that lies above the triangle with vertices…

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Q: Find a parametrization of the circle of radius 5 parallel to the yz-plane with center (-1, 4, 6).

A: The general form of a parametrization of the circle of radius r parallel to yz-plane with center…

Q: cally integra then in any ng curves is

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Q: 82. Use Theorem 6.10 to prove that a sphere of radius 5 has surface area 1007.

A: Given ,radius of sphere=5 We know, surface area (S) of a sphere of radius r units is given by:…

Q: Find an arc length parameterization of the circle in the plane z = 9 with radius 4 and center (1, 4,…

A: The parametrization of the circle in the plane z=9 is:                                   r(t)=⟨1, 4,…

Q: The equation of the tangent plane at the point P(1, 1,-1) on the surface z = f(x, y) = 4 - -* is x +…

A: As per bartleby guidelines we are supposed to answer only one question per post. This post contains…

Q: Consider the integral (image 1) where C is the non-closed curve given by the upper portion of the…

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Q: Use cross products to find the area of the quadrilateral in the xy-plane defined by (0, 0), (1, −1),…

A: Let vertex of Quadrilateral are O(0,0), P(1,-1), Q(3,1) and R(2,4)      Area of the…

Q: Find an equation of the tangent plane to the surface z = In(x - 2y) at the point (3, 1,0) %3D

A: Given that, z = ln (x - 2y) we have to find the equation of tangant at point (3, 1, 0).

Q: Find the points on the surface ry + yz + zr - r - z = 0 where the tangent (5) plane is parallel to…

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Q: Sketch the surface 2./4- and verify that fry - lyx

A: Given surface is  z=4-x2-y2 we have to sketch this and verify that fxy=fyx

Q: Screen. 28 Green's theorem is applicable to ans. yz-plane ху-plane All of these Zx-plane O Previous

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Q: 5 – 4z Show that the reactiob w= transformation the circle z =1 4z -2 in to a circle of a radius…

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Q: Sketch the surface x = 2y2 +3z2

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Q: Show that the area of the plane region bounded by the curves,  x - y =7   and    x= 2y² - y + 3…

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Q: classify the quadric surface given by equation and determine its standard form.−8x 2 − 8y2 + 10z2 +…

A: We have the quadratic surface : -8x2-8y2+10z2+32xy-4xz-4yz-24=0…

Q: Does the product of inversion in the circle of radius 1 centered at the origin with inversion in the…

A: Does the product of inversion in the circle of radius 1 centered at the origin with inversion in the…

Q: (1 point) Calculate the volume under the elliptic paraboloid z = 2x2 +3y2 and over the rectangle R =…

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Q: . Find the area of the surface generated when the curve y = x* 1 + ,on [1,2] is rotated about the…

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Q: What is the surface area of the portion of the surface z=x2+y that lays over the triangle on xy-…

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Q: Find the exact area of surface obtained by rotating the curve about the x-axis. y=sqrt5-x   3< x <…

A: consider the equation

Q: Find a parametrization of the circle of radius 7 with center (5, 3, 9) in a plane parallel to the…

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Q: Find a parameterization for a circle of radius 4 with center (-4,4,-6) in a plane parallel to the yz…

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Q: Identify a generating curve on the rz-plane for the surface of revolution with equation 1² + y² + zª…

A: The equation of the surface of revolution given is as follows:…

Q: By using Cauchy's integral formulas evaluate sin Tz2 + cos TZ² dz (z + 1)(z – 2) C and e2z dz (z –…

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Q: Show that the area of the plane region bounded by the curves,  x=y^2 -1,  x= 1 - y^2  is 8/3 square…

A: Given equation of cyrves, x=f(y)=y2-1,x=g(y)=1-y2

Q: Evaluate the line integral a xds where C is one quarter of a circle (in the first quadrant) of…

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Q: Determine the area of the surface of revolution of x=sqrt{y} from (1,1) to (2,4), rotated about the…

A: The equation is x=y.   Determine the derivative dxdy=12y   The formula for the area of surface…

Q: Find the area of the surface generated by revolving the curve y = Osxs2, about the x-axis. 9

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Q: Let 3 : (3t, r = be a curve in 3-dimensional space having unit tangent and normal vectors u and .…

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Q: Find the area of the surface generated by revolving the curve y=2/x 18xs2, about the x-axis.

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Q: Find the radius of curvature of 6y = x3 at the point (2,). %3D

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Q: Find parametrization of the horizontal circle of radius 4 with center (5, -2, 6). r(t) = %3D

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Q: Evaluate the double integral. (8x – 6y) dA, D is bounded by the circle with center the origin and…

A: The given data is: ∫∫D8x-6ydA To evaluate the double integral.