(1)Calculate the scalar curl of the vector field. F(x, y) = sin(x)i + 6 cos(x)j (2) Let F(x, y, z) = (2exz, 3 sin(xy), x7y2z6). (a) Find the divergence of F. (b)Find the curl of F. -/3 points v MARSVECTORCALC6 4.4.017. My Notes Ask You Calculate the scalar curl of the vector field. F(x, y) = sin(x)i + 6 cos(x)j -/8 points v MARSVECTORCALC6 4.4.023. My Notes Ask You Let F(x, y, z) = (2x2, 3 sin(xy), x?y2z6). (a) Find...
3. Consider the functions \(f(x, y, z)=x y z\) and \(\mathbf{F}(x, y, z)=y z^{2} i+x^{2} z j+x y^{2} k\). Determine which of the following operations can be carried out and find its value:div \(f, \operatorname{grad} f,\) div \(\mathbf{F},\) curl div \(\mathbf{F}\) and div curl \(\mathbf{F}\).
Chapter 15, Section 15.1, Question 018 Find div F and curl F. F(x, y, z) = xz® i + 3y0j +3zyk Enter the exact answers. Enter a value in each entry area, even if the coefficients are 0 or 1 for curl F. div F= Edit curl F = ( ? Edit Di+l ? Edit j+( ? Edit k
Let F 10i4u 8zk. Compute the civergence and curl of F. , div F , curl F Show steps (1 point) Let F (8y2)i(7xz)j+(6y) k Compute the following: A div F В. curl F- i+ k C, div curt F= Note: Your answers should be expressions of x, y and/or z; e.g. "3xy" or "z" or 5 (1 polnt) Consider the vector field F(r,y, ) = ( 9y , 0, -3ry) Find the divergence and curl of F div(F) VF=...
let f=cos^2(x)i+yj+z^2sin(x)k. calculate div(f) and curl(f)
96. Consider a vector field F(x, y, z) =< x + x cos(yz), 2y - eyz, z- xy > and scalar function f(x, y, z) = xy3e2z. Find the following, or explain why it is impossible: a) gradF (also denoted VF) b) divF (also denoted .F) c) curl(f) (also denoted xf) d) curl(gradf) (also denoted V x (0f) e) div(curlF) (also denoted 7. (V x F))
Use Stokes' Theorem to evaluate curl F. ds. F(x, y, z) = zeli + x cos(y)j + xz sin(y)k, S is the hemisphere x2 + y2 + z2 = 4, y 2 0, oriented in the direction of the positive y-axis.
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...
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.
#7, #11, #17 please Calculating the Curl and the Divergence In Exercises 1-20, calculate curl F and divF of the given vector fields F. F = 1 1. F= (°yz?, xyz, wy) 2. F= (x+y23, xyz2, xz) 3. F= (zey, well, ye**) 4. F = (xeyz, zety, ye** ) 5. F= (xsin yz, y sin xz, zsin zy) 6. F = (y sin uz, e sinyz, 2 sinxy) 7, F = (sin x cos z, sin y cos x, sin...