Problem 10 (streamlines, Haberman 2.5.25-26) Again consider (x,y) = -alva+y -y (1- and the associated velocity field v = (vy, -v2). Assume a > 0. (a) Define V(r, 0) = (r cos0, rsin0). Determine the domain H of V and plot nu- merically the level sets Ch = { (r, 0) E E : V(r, 0) = h} CE and In = {(x, y) Eu : (x,y) = h} cu for a = h = 1/2. (b) Show that for every h E R and a > 0, the level set L, contains a curve y : (a, b) - l with lim |7(t)| = 00. (6) In (6) the limit is taken as the parameter t tends to some limit T. Setting y = (71, 72) determine lim 92(t). (c) A stagnation point is a point (x, y) ( U for which v(x, y) = 0. For which values of a will there be a stagnation point on Ou ? (d) Consider Lo = {(r, 0) E E : V(r,e) = 0} CE and Lo = {(x, y) Eu : (x,y) = h} cu. Write down (carefully) a formula for each of these curves