Question

PLEASE I NEED HELP WITH THIS CALCULUS 3 HOMEWORK

Homework Set 10 DUE: MAY 4, 2020 (1:00PM EDT VIA BLACKBOARD) To be handed in: Please write your solution to Problem 1 on a single sheet of paper! 1. Determine if the following vector fields F: 22 CR" + R" are conservative. In case they are conservative, Ifind a potential function f, that is, such that F = Vf. a) f(x,y) = (zy, xy), =R² b) F(x, y, z) = (zey, 2x sin(2), x +z+1), N=R3 c) F(t, y) = (e” cos y, -e* siny), N=R?

Answer 1

DXFE ! 5 K 1% % %3 I fi fa fa and method @ OXF=); ó K 1 Flary) zlały, xyy 1 %a %y ha E x²y it aghj tk (6) Tazy aye ol jPzxyz de A zif0-0)-3(0-0) + ( (45°)-(x+y)]azayan mga ay Txł zł(y 2_22) to Then GVF is not Consewater Fri not. a. conservation (Ems not Irrotational Vector) . ® F (3,3,3)= (3e, 22 Sün 2, 2+3+1) Fri (key) + ģ (22 si ) + F (a +3+) OXF=li ý k 1. les 24 hizo atžti 1 =(1+3+) – g (525x3] ]-3} (2424) - (te) + K (da (23ia) 2(.) 7(0-2248) - 5[ite, nev] +R(2.57 2-3 e] EXE = -2x cosa T-j (1-0))+ R (asmi & Zey OXF to a É is not conservative © FR, y) = (edas y easy) Let paelany - of y = - e? Sunt És el cobyi-et sammen ! Bre's 4 = esny p=Q - Ind method . the Given vector field i - Conservation

(#2) VXFal i j k l Teclady etsing on e lekary ze say =i[0-0)-5[0-0] + R[-esseny te sien] Xezo - Î û an Irrotational velot (6) Conservations In conservative field VXFFO , oft=0 Ex(TP) 20 its Ē The ett kort a easyi-eľstva na en elasy, se sont Scalar potential df = 1 of ander + fotos de da S&t= sercosy do + fret Samy dy fa ea casy -e? (-as) te asf = 2ematyta scale potential f= elasyte