For the two functions
$$f\left( {x,y} \right) = {x^3} - 3x{y^2}\,\,$$ and $$\,\,g\left( {x,y} \right) = 3{x^2}y - {y^3}\,\,$$

Which one of the following options is correct?

At $$x=0,$$ the function is $$f\left( x \right) = \left| {\sin {{2\pi x} \over L}} \right|\left( { - \infty < x < \infty ,L > 0} \right)$$

The function $$f\left( x \right) = {x^2} = x + x + x + ....x$$ times, is defined

At $$x=0,$$ the function $$f\left( x \right) = {x^3} + 1$$ has