\displaystyle \lim_{(x,y,z) \to (0,0,0)} \frac{\| f(x,y,z)-f(0,0,0)-0((x,y,z)-(0,0,0))\|}{\|(x,y,z,)\|}=\displaystyle \lim_{(x,y,z) \to (0,0,0)} \frac{|\frac{x^2y^2z^2}{x^4+y^4+z^4} |}{\sqrt{x^2+y^2+z^2}}