How can I show that the limit of the following function, when the variables `{x, y}` tend to zero, is zero? Mathematica gives the error 

>{x,y} is not a valid variable. 

Domains are $0<x<10$ and $0<y<1$.
```
Limit[Cosh[1/Sqrt[y]] Sinh[x/Sqrt[y]] - y Cosh[x/Sqrt[y]], {x, y} -> {0, 0}]
```
Any comment is welcome.