MATH 216 Lecture 19: L19 Section 4.1, 4.2

(1 pt) Consider the vector field F (x, y, z) = xi + yj + zk. a) Find a function f such that F = Vf and f(0,0,0) f(x, y, z) = b) Use part a) to compute the work done by F on a particle moving along the curve C given by r() = (I +4sin t) i + (1+sin2 t)j+(1+sin3 t) k, 0 t 플

Consider F and C below. F(x, y) = xy,2 i + x2yj C: r(t) = , 0 (a) Find a function f such that F = t 1 (b) Use part (a) to evaluate Jc Vf dr along the given curve C.

Consider F and C below. F(x, y, z) = yze®i + exzj + xyexzk, C:r(t) = (t2 + 2)i + (t2-1)j + (t2-2)k, (a) Find a function f such that F = Vf. rx, y, z) = 0 t 2 Use part (a) to evaluate