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)):}

Question

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)):}

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(Solved): Which of the following functions is continuous at (0,0) ? (i) f(x,y)={((x^(8)y^(6))/(x^(8)+2y^(2)) ...