Let Calculate vector field F divergence. V.F= Let where n on the edge S = OV outward-facing unit normal. Also calculate the following surface integral: ICF S (F.n) dS = F(x, y, z) = (5xi +y³j−5zk). V = {(x, y, z) | −1 ≤ z ≤ 1, x² + y² ≤ 1},

Q: Evaluate the line integral SF dr, where F(x, y, z) = -2xi + 3yj - zk and C is given by the vector…

A:

Q: List different ways to write the work integral for F = Mi + Nj + Pkover the curve C: r(t) = g (t)i +…

A: Given a vector field and a curve C. We need to find different ways to write the work integral for…

Q: 7. Let F be the fluid force on a side of a semicircular plate of radius r meters, submerged…

A: (a) Redraw the diagram a follows:

Q: (b) Use a theorem to find [F.dr. Which theorem did you use? Evaluate completely. Indicate the…

A:

Q: Answer the following True or False: Let f(x, y) be differentiable at (zo, 30). Then the vector is a…

A: The equation of the tangent plane to the surface f(x, y, z)=0 at x0, y0, z0 is defined as: fxx0, y0,…

Q: (e) If E C R³ is the ellipsoid (x/2)2 + (y/3)² + (z/4)² = 1 and F evaluate the integral ffE curl F-…

A:

Q: Let z = g(z, y) = f(3 cos(ry), y + e") provided that f(3, 7) = 4, fi(3, 7) = 2, f2(3, 7) = 3. i)…

A: Let z=gx,y=f3cosxy, y+exy f3,7=4, f13,7=2, f23,7=3

Q: 1. Consider the surface defined by z = x2 + e9y ln(x-y). Let f(x,y) =  x2 + e9y ln(x-y). ○ Compute…

A: The given problem is to find the gradient vector of the given surface at point and to find the…

Q: Q6|| Find the tangent plane and normal line of the surface x+y+z=1 at the point p(0,1,0).

A: Equation of tangent plane is Fx(x-x0) +Fy(y-y0) + Fz(z-z0) =0  F = f(x, y) =k

Q: Let z = g(x, y) = f(3 cos(xy), y + ev) provided that f(3,6)= 7, f₁(3,6) = 2, f₂(3,6)= 5. i) Find g₁…

A: note :Since you have posted multiple questions, we will provide the solution only to the first…

Q: Evaluate the line integral f F dr, where F(x, y, z)= -sin xi - 3 cos yj+xzk and C is given by the…

A:

Q: Draw a contour plot for f(x, y) = xy. Include contour lines at z = ±2, ±1, 0. On top of this contour…

A: The contour lines are the method used to draw the graphs in three dimensions in the two-dimensional…

Q: 1. Determine the velocity field v so that the surface F(r, y.t) = (y+t)+ (z+t)? - a² = 0 to be a…

A: The given surface is - F(x,y,t) = (y+t)2 + (x+t)2-a2.......(1) The velocity field (V→) components…

Q: Q1: Find the tangent plane and normal line of the surface F(x,y,z)=x² + n + y² + z² 10 at point…

A: We have to calculate partial derivatives first.

Q: Evaluate / . F. dS Is where F = and the surface S is the triangle with vertices (1, 1, 0), (0, 2,…

A: Given To evaluate ∬SF.dS  where F=<x+1,-1-2y,z> and the surface S is the triangle with the…

Q: Let C' be the circle centered at the origin with radius 3 oriented clockwise, and let F(x, y) = (−7x…

A:

Q: Evaluate the line integral faF · dr, where F(x, y, z) = -2xi – 5yj + 5zk and C is given by the…

A:

Q: P. Consider the following vector.field F(x.y).and compute the line integral over C, where C is an…

A:

Q: H.W: find the tangent plane and normal line of the surface f(x, y, z) = x² + 2xy – y² + z? = 7 at…

A: The function is given is fx,y,z=x2+2xy-y2+z2  gradient vector, ∇F=fx,fy,fz ∇F=2x+2y, 2x-2y, 2z and…

Q: Evaluate the line integral F. dr, where C is given by the vector function r(t). Jc F(x, y) = xy i +…

A:

Q: If F(x, y, z) = z - f(x, y) and s is the graph of z = f(x, y) and (a, b,c) is a point on the surface…

A:

Q: Use Stokes' theorem to calculate the integral for the surface S and boundary aS, and the given…

A: S={(x,y,z): x2+y2+z2=64, z≥0} This is an equation of a sphere We take an element in the (x,y) plane…

Q: dz 2) Evaluate the line integral where c is a unit circle (1–z)3’

A:

Q: Find all points where the surface z = xy e-* + 2y-) has a horizontal tangent plane. %3D O A. O B.…

A: Given the surface

Q: Harry fills up his Jeep with gasoline and notes that the odometer reading is 23,511.9 miles. The…

A:

Q: segment from ( 0,3,0) to (1, 3,7).Use line integral and check answer by caleulating (s.y.)

A: