This problem is an example in my calculus textbook. Let:
$$
f(x,y)=\frac{y^2\sin^2(x)}{x^4+y^4}
$$
My textbook says that
$$
\lim\_{(x,y)\to(0,0)}f(x,y) \text{ does not exist.}
$$
**Questions:**

1. How do we know the limit does not exist?
2. In general, suppose the limit of a function exists but we do not know the value of such limit, how do we find it?