RELI 125 Lecture 7: the origins of Satan

(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)i 2y arctan(x) j 1 + X c: r(t) = t2 i + 3t j, 0 t 1 (a) Find a function f such that F = Vf f(x, y) = |y?arctan(x) 2 (b) Use part (a) to evaluate V. dr along the given curve C.

Consider F and C below. F(x, y, z) = yze®i + exzj + xyexzk, C: r(t) = (t2 + 4)i + (t2-1)j + (t2-5)k, (a) Find a function f such that F = Vf rx, y, z) = 0 t 5 (b) Use part (a) to evaluate F dr along the given curve C