Let C be a simple closed smooth curve in the plane 2x + 2y +z =2 oriented as shown on the right. Show that 2x + 2y + z-2 O, 2y dx + 3z dy – x dz depends only on the area of the region enclosed by C and not on the position or shape of C. ..... Let C be an arbitrary path x(t)i + y(t)j + z(t)k in the given plane. Then r can be expressed as xi + yj + zk and the integrand of 2y dx + 3z dy - x dz is F• dr where F i+

Q: Evaluate Se (5xy + x² + y²) dx + (x² - y)dy by using Green's theorem, where C is a closed curve that…

A:

Q: Find a plane containing the point (7,3,5) and the line x(t) - 3 + t | y(t) 8 +t z(t) - 3 + 5t

A:

Q: c) The surface S is the portion of the plane x+y+z=1 in the first quadrant of the Oxyz Cartesian…

A: Given: The surface and curve is shown below   The region s is the triangle and the curve C is the…

Q: Let C be the positively oriented closed plane curve consisting of the line segment from (-3,0) to…

A:

Q: Let F= (0,0, z) and S be the part of the paraboloid z = x² + y² between the plan z = 1 and 2 = 4,…

A:

Q: Let C be the closed curve indicated in the diagram. Use Green's Theorem (2,1) (o,i) (x² + y?, y³ +…

A:

Q: Q2/ Find T, N, and k for the space curve r(t) = (3 sin t)i +(3cos t)j + 4tk

A: Question: Objective is to calculate the tangent vector T, normal vector N and the curvature κ of…

Q: Calculate dz – yz dy – sen(2)dz, where Cis the path connecting the point A(-2, 2, 4) to the point…

A:

Q: Find B and t for the space curve r(t) = N 11 ਕਰਜ |·+|· 1 +1 + 2 3 ()+( 3 +1 j, t> 0.

A:

Q: The line of intersection of the planes x + y + z = 0 and x - y = 0 is

A: The given planes are..Find the equation of the line in parametric form.

Q: Evaluate the line mtegral over the curve S(-x + y +z) dx + (x+y - z) dy + (x-y +z) dz where the line…

A:

Q: Please review the screenshot and provide a solution. Please make sure that the solution is formatted…

A: Approach: Understand the problem statement:The goal is to evaluate the integral ∫f(x,y,z)ds over a…

Q: Let f(z) = E (z – 5)" n4" (n + 2)2 n=1 i) ii) iii) Find the region where the function f(2) is…

A: The boarder of the image looks like square root of the term. But not it is square root. Please check…

Q: Consider the piecewise smooth curve C = C1 u C2 u C3 u C4, oriented from the point A(1, 1, 2) to…

A: Given that, F=4x3-2z, 3y2,-2x Find the value of ∫cF. dr we have to find the function f such that…

Q: Let F = (4x³ + yz, xz, xy). Let C be any smooth curve from (1, 1, 1) to (2, 3, 0) Calculate cF dr.

A:

Q: Let L, be the line through the points (1,2,6) and (2,4,8). And let L2 be the line of intersection of…

A:

Q: the space curve (t) = (2t, t², 2t)

A:

Q: Explain why you think the series Σ01 -1)! (n+1)! converges to a finite number or diverges. If the…

A:

Q: Evaluate F-di where F(x, y, z)=1li +(x+yz)j+(xy- Vz 3x+2y+z=6 in the first octant. C is a positively…

A: Here we have to evaluate ∫CF→·dr→=? Where F→(x,y,z)=i^+(x+yz)j^+(xy-z)k^ and C is the boundary of…

Q: Let P be the tangent plane to the surface z=2x2+y2 at the point Q=(1,1,3). Which of the following…

A: tangent planes to a surface are planes that just touch the surface at the point and are “parallel”…

Q: A. Let f(x, y, z) = z²-x² - y² .The set of all values of c such that the level surface f(x, y, z) =…

A: