Use the gradient rules to find the gradient of the given function, f(x,y,z) = x+yz y+xz...
Consider F and C below. F(x, y, z) = yz i + xz j + (xy + 10z) k C is the line segment from (3, 0, -3) to (4, 4, 1) (a) Find a function f such that F = Vf. f(x, y, z) = (b) Use part (a) to evaluate [s vf. dr along the given curve C.
8Two vector fields are given: F(x,y,z) - (esin(yz), ze* cos(yz), ye* cos(yz)) and F(x,y,z) = (z cos y, xz sin y, x cos y). a) Determine which vector field above is conservative. Justify. Foly = fjol so, <ea sin(J2), 20% cos(82), y acos (92)) Conservative. b) For the vector field that is conservative, find a function f such that F - Vf. Lxelsing2, zetos yea, yet cosy 2 c) Use the Fundamental Theorem of Line Integrals to find the work...
Find a formula for the distance from the point P{x,y,z) to each of the following planes. a. Find the distance from P(x,y,z) to the xy-plane. b. Find the distance from P(x,y,z) to the yz-plane. c. Find the distance from P(x,y,z) to the xz-plane. a. Choose the correct formula for the distance from the point P(x,y,z) to the xy-plane. O A. Iz OB. Mx2 + y2 OC. Vz OD. x² + y² + 2? b. Choose the correct formula for the...
F(x,y,z) =< P, Q, R >=< xz, yz, 2z2 > S: Bounded by z = 1 – x2 - y2 and z = 0) Flux =SS F ñds S (8a) Find the Flux of the vector field F through this closed surface.
Please explain (1 pt) Use Stokes' Theorem to find the circulation of F = (xy, yz, xz) around the boundary of the surface S given by z 0 x 4 and -2 < y < 2, oriented upward. Sketch both S and its boundary C 16 - x2 for Fdr = Circulation = (1 pt) Use Stokes' Theorem to find the circulation of F = (xy, yz, xz) around the boundary of the surface S given by z 0 x...
I. a) (4 points) For a given function F(x, y, z) = xz + (y + z)(x + z) Draw the logic circuit diagram of the function: b) Using Boolean Algebra to simply the above function c) Use Demorgan's Theorem to find out the complement of the above function F(x,y,z)xz+ + 2)(x +z)
let F(x,y) = <2x+yz,xz-2y,3z^2+xz> find the potential function.
If x, y, and z ∈ Z show that (x + y)z = xz + yz, where x = (a, b), y = (c, d), and z = (e, f)
5. Let F(x, y, z) = (yz, xz, xy) and define Cr,h = {(x, y, z) : x2 + y2 = p2, z = h}. 1 Show that for any r > 0 and h ER, Sony F. dx = 0
9. If f(x, y, z) = x sin yz. (a) (2 points) Find the gradient off (b) (3 points) Find the directional derivative off at (1, 3, 0) in the direction of v= i +2j – k.