Question

Please help me with these questions, show working. thank you

I-(8z2+3e3rcos(5y) i-( 5e3rsin(5y)) j+16xz k The vector field I is conservative, find a scalar potential function f(x.y,z) such that I grad f and f(0,0,0) 1 Your answer should be expressed using the correct Maple syntax; for example, it might be: 2*x^2"y+5*z*exp(-9*y) cos(4*z) Do not use decimal approximations all numbers must be correct Maple expressions. The scalar potential is f(x,y,z) Skipped Change the order of integration and evaluate the following double integral: (45.ona e/5) dy C/3) 1 12 dx. Your answer can be expressed as a number accurate to five significant figures or as an expression in correct Maple syntax. For example: 15*(exp(1/4)-1)/7 OR 0.608625894 OR rounded to 0.60863 | = Skipped Use Green's theorem in the plane to evaluate K=(y d(tie+139) dy 2 3Cy K = anti-clockwise around the closed path C given by the curves: y-0, 0 s xs 2, .r= 2, 0 s0 s TT/6, .0 TT/6, 2 2 r2 0. Evaluate the line integral as a double integral using polar coordinates. Your answer should consist of a single number accurate to five decimal digits or as an exact rational expression. For example: 10.13906368 OR rounded to 10.13906 OR 3 Pi+5/7 Skipped K

Answer 1

(822+3 e Mo (82+ 8 e3 tos 32 ces(sy)i-(5e in 2 sin5y) En -Se N 2 Pa 1622 SMdr 32 3 e S C82 ces(syp) da eos(Sy 2 32 + 3e 3 32 + e 8スー cos (sy) sin (5y) g'2) 22 -5e ニN 32 -se aintsj - Se sin (sy)a') ht2)

e Cos + 8xazxa t0h(2) L622+h102 162z th'12) 1622 eC constart h(2) 32 + e ces (5yc + C cos (Sxo) + C 8 X6XO+e 1 e coso t C O+1 +C 1 1 secertoy) Scalar 32 8z2 2te patential