Use Green’s Theorem to evaluate the line integral Z C−→F . d−→r , where C is the circle x^2 + y^2 = 25 oriented clockwise, and −→F (x, y) = (e^x + x^2y)−→i + (e^y − xy^2)−→j .

Q: Assume S is the surface x1000 + y8000 + z1000 = 1,000,000 and F = [9 + ee^(xyz), x8yz, 3x - 5y -…

A:

Q: Evaluate ʃC F dr where C is the parabola y = x2 from (0, 0) to (2, 4) and F (x, y) =< −ysinx,…

A: Given a curve C is a parabola from (0, 0) to (2, 4)

Q: Find a point on the surface x+4y--z² =1 where the tangent plane is parallel to the plane x+4y- z =…

A: we need to find gradient of given surface to know about direction of normal vector to tangent plane

Q: 2. Find the equation of the tangent plane to the surface x²+3y²+4z² = 20 (2,2, 1). at the point

A: Step 1:To find the equation of the tangent plane to the surface x2+3y2+4z2=20 at the point (2,2,1),…

Q: Evaluate the line integral (2x-y+6)dx + (5y + 3x - 6)dy, for which the path C traverses C around a…

A:

Q: The door prizes at a dance are ten $10 gift certificates, twenty $20 gift certificates, and five $50…

A: Given that the door prizes at a dance are ten $10 gift certificates, twenty $20 certificates, and…

Q: Find an equation for the tangent plane to the surface x = u² – v², y = u + v, 2 = u² + 4v at (-},2).

A: We have r(u,v) = (u2-v2)i + (u+v)j + (u2+4v)k

Q: x ds, where C is the portion of the parabola from (0,0) to (1, 1), followed by the line segment from…

A:

Q: Consider the Hamiltonian H = H, + AH' E 0 H, =0 E, 0 0 0 E, a) What are the eigenvalues of H,? 0 v 0…

A: Hello. Since your question has multiple sub-parts, we will solve first three sub-parts for you. If…

Q: Evaluate fc 2x ds, where consists of the arc of the parabola y= x2 from to followed by the vertical…

A: The given line integral is ∫C2xdS where C is the arc of the parabola y=x2 from (0,0) to (1,1) and…

Q: Find the trace of the surface 4x^2 − y^2 +6z^2 = 2 in the yz-plane and identify the conic section.

A: Given 4x2-y2+6z2=2

Q: Q1.6 Find the point on the surface given by the equation x^2 + 5y^2 + 10z^2 = 18016 that has a…

A:

Q: Integrate counterclockwise dz, C' the circle with z² + 8z + 15 center -3 and radius 2. dz = La z2 +…

A:

Q: Which surface below is an elliptic paraboloid? O x^2 + y^2/4 - z^2 = 1 O z = -sqrt(x^2 + y^2) z =…

A:

Q: Sketch the surface 1<z</9-x² - y² and x²+y² <1

A: To sketch the given surfaces.

Q: Let F = (3z + 3x²) ¿+ (6y + 4z + 4 sin(y²)) 3+ (3x + 4y + 6e²²) k (a) Find curl F. curl F - (b) What…

A: