This one is giving me such a hard time. I guess this is important to know because it is saying that the square root of the function translates to the square root of the limit. Similar to mutliplication and addition. The hint they give is to use the fact that if all convergent subsequences have the same limit, then the sequence is convergent. I need help on this one. Thanks.
Suppose <x_n> --->x for each natural number n, where x_n >= 0. Prove that <sqrt(x_n)> ---> to sqrt(x)