Show that A Function with a Single Point of Discontinuity 2xy x² +1,²² 0, is continuous at every point except the origin f(x, y) = (x, y) = (0,0) (x, y) = (0,0)

Exercise 1- Determine which of the following functions are analytic: 2 2 d- x²+iy², b = 2xy + i(x²y²) 1 d= (2-1)(2+1) x-iy x²+y2 E- Sinx coshy+icosx sinhy C- )

2x'y+x?y? + 3xy³ 16x4 – ya if (x, y) # (0,0) Let f(x, y) = if (r, y) = (0,0) Determine the set of all points where f is continuous.

Let f(x,y) { and let g(x, y) O x6y6 26+y6 = O { 6x³y³ 6x6 + 6y6 only Which of the above functions are continuous at (0,0)? f only if (x, y) = (0,0) f and g if (x, y) = (0,0) neither if (x, y) = (0,0) if (x, y) = (0,0)