Let S be the parabolic arch given by r(u,v) = (u+v, u-v, 4-u²) where (u, v) € [−2, 2] × [0, 1]. Compute the normal vector xr Here is a picture of this surface. Draw (in several representative places) the direction of the normal vectors that you computed in the previous part of the problem. Set up and evaluate the flux integral of F = j across S. I

Let S be the parabolic arch given by r(u, v) = (u+v, u−v, 4-u²) where (u, v) € [−2, 2]×[0, 1]. Compute the normal vector × ди Iv' Ər Here is a picture of this surface. Draw (in several representative places) the direction of the normal vectors that you computed in the previous part of the problem. Set up and evaluate the flux integral of F = xj across S.

−Y+z5 Let F (x, y, z) := x+yz7 3+2⁹ let ʼn be the outward unit normal vector. Evaluate ſf (curl F) · ndS. (Use syntax like 2*pi/3 .) Let S be the upper half of the sphere of radius 2 centered at the origin. At each point of S

Find a vector function that represents the curve of intersection of the two surfaces. The cone y = V = v 2x2 +9z2 and the plane y = 5+3z r(t) = ( 1 t2 2' 15 6. 1 r(t) = (t, 1 t2 2' 15 6. 1 5 r(t) = (! + 구 t, 15 %3D 6. r(t) = (t, - + 2' 15 6. r(t)%3D = ( t, ť + 15 6.

The vector v = <a, 1, -1>, is tangent to the surface x2 + 2y3 - 3z2 = 3 at the point (2, 1, 1).  Find a.

Let S be the parabolic arch given by r(u, v) = (u+v, u−v, 4−u^2) where (u, v) ∈ [−2, 2]×[0, 1]. Compute the normal vector ∂r/∂u × ∂r/∂v . Here is a picture of this surface. Draw (in several representative places) the directionof the normal vectors that you computed in the previous part of the problem. Set up and evaluate the flux integral of F = x j across S.

Find a vector normal to the surface x2 + yz = 5 at (2, 1, 1).

Find symmetric equations of the normal to the surface, r (u, v) = < u2, v2, u + 2v > at a point (1, 1, 3)

Let the temperature in degrees at the point (X,y,z), with distances measured in cm, be T(X,y,z)=5x – 4y +3z. Let 9 be the real number such that the rate at which the change in temperature at (1,0,3) per unit change in the distance travelled in the direction of the vector (1,q,1> is 4 /cm. Find . (Note that the "direction" of a vector is always a unit vector "pointing the same way.") none of the other answers -7/40 17/56 1/12 1/2

Check that the point (1,-1,2) lies on the given surface. Then, viewing the surface as a level surface for a function f(x, y, z), find a vector normal to the surface and an equation for the tangent plane to the surface at (1,-1,2). vector normal = tangent plane: 4x² - y² +3z² = 15