Problem 10 (streamlines, Haberman 2.5.25-26) Again consider (I,y) = -alva+y -y (1- 7 2 + y and the associated velocity field v = (ty, -12). Assume a > 0. (a) Define V(r, 0) = (rcos, rsin0). Determine the domain H of I and plot nu- merically the level sets Ch = {(r, 0) E E : V(r, 0) = h} CE and Ln = {(x, y) El : (x,y) = h} cu for a = h = 1/2. (b) Show that for every h ( R and a > 0, the level set L, contains a curve y : (a, b) - l with lim ly(t)| = 00. (6) In (6) the limit is taken as the parameter t tends to some limit T. Setting y = (71, 72) determine lim 12(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