Let $S\in R^{n}$ is a set and $x\in S$. We define tangent cone of $S$ in $x$ as: $$T_{S}(x)=\{z\in R^{n}:\exists (x_{k}), x_{k}\in S, x_{k}\rightarrow x, \exists (y_{k}), y_{k}>0, y_{k}(x_{k}-x)\rightarrow z\} $$ I don't understand the definition very much. I am supposed to find the tangent cones for the following sets at the point $[0,0]$: $A=\{(x,y):x\geq - y^{3}\}$ $B=\{(x,y):x\in Z, y=0\}$ $C=\{(x,y):x \in Q, y=0\}$
Does anyone know the solution? Thanks in advance.