Determine the set of points at which the function is continuous:

Question

f (x, y) = {(x²y³)/(2x²+y²) if (x, y) ≠ (0, 0) & 1 if (x, y) = (0, 0)

Answer 1

The discontinuities happen when the denominator is equal to zero. So...

2x² + y² = 0

Should produce someone that looks like

y = ± x√2

This produces a pair of lines with slope ±√2, and everything outside that should be continuous