$\underset{(x,y)(0,0)}{lim}\frac{y^4-2x^2}{y^4+x^2}$

What value does $f(x,y)=\frac{y^4-2x^2}{y^4+x^2}x,yx-$axis? Select the correct choice below and, $if$ necessary, fill $in$ the answer box $to$ complete your choice.

$A.f(x,y)$ approaches $(Simplify$ your answer.$)$

$B.f(x,y)$ has $nolimit$ and does not approach $or-as(x,y)$ approaches $(0,0)$ along the $x-$axis.

What value does $f(x,y)=\frac{y^4-2x^2}{y^4+x^2}$ approach $as(x,y)$ approaches $(0,0)$ along the $y-$axis? Select the correct choice below and, $if$ necessary, fill $in$ the answer box $to$ complete your choice.

$A.f(x,y)$ approaches $(Simplify$ your answer.$)$

$B.f(x,y)$ has $nolimit$ and does not approach $or-as(x,y)$ approaches $(0,0)$ along the $y-$axis.

Why does the given $limit$ not exist?

$A.As(x,y)$ approaches $(0,0)$ along different paths, $f(x,y)$ approaches two different values.

$B.As(x,y)$ approaches $(0,0),$ the denominator approaches $0.$

$C.As(x,y)$ approaches $(0,0)$ along different paths, $f(x,y)$ does not always approach a finite value.

$D.As(x,y)$ approaches $(0,0)$ along different paths, $f(x,y)$ always approaches the same value.