Solve Laplaces equation inside a circular cylinder subject to the boundary conditions (a) u(r, , 0) = (r, ), u(r, , H) = 0, u(a, , z)=0 *(b) u(r, , 0) = (r) sin 7, u(r, , H) = 0, u(a, , z)=0 (c) u(r, , 0) = 0, u(r, , H) = (r) cos 3, u r (a, , z)=0 (d) u z (r, , 0) = (r) sin 3, u z (r, , H) = 0, u r (a, , z)=0 (e) u z (r, , 0) = (r, ), u z (r, , H) = 0, u r (a, , z)=0 For (e) only, under what condition does a solution exist?

L14 - 10 NOTE: x y = e (a,e ) 2 ex. Find g (x)f i g(x)= ex +2 e + xe + x . 2 e Now You Try It (NYTI): Find the derivatives of the given function. x e (a) f(x)= e (b) f(x)= x (c) f(x)= e (d) f(x)= ex √ (e) f(x)= ex