Question 8: Is the fuction f(x, y) = - x²y x²+y² if (x, y) = (0, 0), if (x, y) = (0,0) Continuous? Explain why.

Consider the function. f(x, y) = 2(y + 1)x² Identify the point(s) on the graph of f at which the tangent plane is horizontal. (0, 2) (x, 0) for only x ≥ 0 (x, 0) for all x (0, y) for all y (2,0)

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)