do the three with mark
1.31. Show that the union of two regions with nonempty intersection...
1.31. Show that the union of two regions with nonempty intersection is itself a region. 1.32. Show that if ACB and B is closed, then dAC B. Similarly, if AC B and A is open, show that A is contained in the interior of B 1.33. Find a parametrization for each of the following paths: (a) the circle C[1+ i, 1], oriented counter-clockwise (b) the line segment from -1-to 2 (c) the top half of the circle C[0, 34], oriented clockwise (d) the rectangle with vertices 12i, oriented counter-clockwise (e) the ellipse z EC: |z-1+|z+1= 4}, oriented counter-clockwise 1.34. Draw the path parametrized by r)cos()cos()+ i sin(t)sin(t)|
1.31. Show that the union of two regions with nonempty intersection is itself a region. 1.32. Show that if ACB and B is closed, then dAC B. Similarly, if AC B and A is open, show that A is contained in the interior of B 1.33. Find a parametrization for each of the following paths: (a) the circle C[1+ i, 1], oriented counter-clockwise (b) the line segment from -1-to 2 (c) the top half of the circle C[0, 34], oriented clockwise (d) the rectangle with vertices 12i, oriented counter-clockwise (e) the ellipse z EC: |z-1+|z+1= 4}, oriented counter-clockwise 1.34. Draw the path parametrized by r)cos()cos()+ i sin(t)sin(t)|