Determine all points at which the given function is continuo

Determine all points at which the given function is continuous. Please explain your answer

Determine all points at which the given function is continuous. {(x, y)|x + y 0} {(x, y)|x - y 0} {(x, y)|x, y are each any real number } {(x, y)|x2 - xy + y2 0}

Solution

c) you have to check coontinuity at points where definition changes that is at x+y=0 (x^3 + y^3)/(x+y) = x*x + y*y - xy now put limit x+y =0 or y = -x 3x*x which is equal to -3xy : -3x(-x) = 3x*x hence continuous for all vlaues of X and y