Which of the following functions is continuous at $(0,0)?$

$($i$)f(x,y)=\{\begin{array}{ccc}\frac{x^2{y}^4}{x^2+5y^6}& if(x,y)(0,& 0)\\ 0& if(x,y)=(0,& 0)\end{array}$

$($ii$)g(x,y)=\{\begin{array}{ccc}\frac{xy}{x^2+6y^2}& if(x,y)(0,& 0)\\ 0& if(x,y)=(0,& 0)\end{array}$

$($iii$),h(x,y),=\frac{\sqrt[\phantom{2}]{x^2+y^2+1}-1}{x^2+y^2}if(x,y)(0,0)$

$\frac{1}{2}if(x,y)=(0,0)$

$($A$)($ii$)$ and $($iii$)$ only

$($B$)($i$)$ and $($iii$)$ only

$($C$)($i$)$ only

$($D$)$ all of them

$($E$)$ none of them

$($F$)($i$)$ and $($ii$)$ only

$($G$)($ii$)$ only

$($H$)($iii$)$ only

Problem #$7$