Home /
Expert Answers /
Calculus /
which-of-the-following-functions-is-continuous-at-0-0-i-f-x-y-x-8-y-6-x-8-2y-2-pa294

Which of the following functions is continuous at

`(0,0)`

? (i)

`f(x,y)={((x^(8)y^(6))/(x^(8)+2y^(2)) if (x,y)!=(0,0)),(0 if (x,y)=(0,0)):}`

(ii)

`g(x,y)={((xy^(5))/(x^(6)+4y^(6)) if (x,y)!=(0,0)),(0 if (x,y)=(0,0)):}`

(iii)

`h(x,y)={((\sqrt(x^(2)+y^(2)+9)-3)/(x^(2)+y^(2)) if (x,y)!=(0,0)),((1)/(6) if (x,y)=(0,0)):}`