Σ 96 5 96 LL N 6) H. 4. fs 7. 8. 6. 144 f12 where C is the line segment from (1,0) to (-1,3). ロ is a conservative vector field. Then find a function f such that F = V f, and use it to evaluate the integral Gus F dr Show that F(x, y) = (ye + sin y) î + (e + x cos y) ĵ Question 5 %3D If the linear density is a constant k, find the mass and center of mass of the wire.

Let f(x, y) = 7x cos (y). Find the conservative vector field F, which is the gradient of f. (Give your answer using component form or standard basis vectors. Express numbers in exact form. Use symbolic notation and fractions where needed.) F = (7 cos (y).-7x sin(y) Evaluate the line integral of F over the upper half of the unit circle centered at the origin, oriented clockwise. (Give an exact answer. Use symbolic notation and fractions where needed.) C F. dr = Incorrect 12 Question Source: Rogawski 4e Calculus Early Transcendentals Publisher: W.H. Freema 5.02. D

6. Denote by V the vector ·(). Then we can define the operations grad (f) = f (gradient of f), div (F) = V F (divergence of F), and curl (F) = ▼ × F (curl of F). (a) Given F = (2x + 3y, 3x + z, sin x), calculate div(F) and curl(F). (b) Is the vector field F = (x + y,3y, z-x+1) conservative? What about F = (yz, xz, xy)? (c) Calculate V × (Vf) =curl(grad f) and V. (V × F) = div(curl F).

True or false.. need asap will rate high