Evaluate the limit: $\lim_{(x,y,z)\to(0,0,0)}\frac{xy+yz^2+xz^2}{x^2+y^2+z^4}$
Along the curve $x=y=z^2$, the function is identically $1$.
Along the line $y=z=0$, the function is identically $0$.
Along the line $x=y, z=0$, the function is identically $\frac 12$.
Along the line $x=2y, z=0$, the function is identically $\frac 25$.