1. For the piecewise function f (ac) = 3 sin x - 2b x1/2 36 - 4 - 4x x>1/2 find the value(s) of b such that f(x) is continuous for all values of x. For any other value of b, f(x) is discontinuous at x = 7/2. What type of discontinuity is this? Is the function differentiable at x = 1/2? Why or why not? 2. Show that 9z = r cos2 0+r2 sin 0 in cylindrical coordinates is equivalent to some z = f (x, y) in Cartesian coordinates. (Use the definitions we derived in class for conversions, not the book, as their definitions are switched for $ and 0). 3. Find all roots of z = V27eTi/2. Write your answer in terms of Re{z} and Im { }. 4. Let f(z) = eliz - iz2 + 2*. Find f in terms of x and y, f*, Re(f), and Im( f)