Ok, so I was reading my Real Analysis Text and there was a proof that Lim sqrt(Xn)=Lim sqrt (X). They had two cases, one where Xn=0 where they use the Delta-Epsilon limit test and it makes perfect sense to me. However, they also show the example where x>0. obviously since x>0, Sqrt(x) is also >0. They prove it without using the E-D method and I am trying to prove it using it. Ill show my first few calculations ill use S(Xn) to denote sq. rt. and e to denote epsilon:
e>0 is given
|S(Xn)-S(x)|<e after multiplying by (S(Xn)+S(x))/(S(Xn)+S(x)) i get: Xn-X/(S(Xn)+S(x))<e now it would also be true that Xn-X/(S(Xn)<e from here, i do not know how to continue the proof in order to solve for it. If i squared both sides, i would have a nasty polynomial on top and that wouldnt offer much help.. any advice?