Proof: sqrt(x) is Continuous using Epsilon Delta Definition | Real Analysis Exercises

We prove that f(x)=sqrt(x), the square root function, is continuous on its entire domain where it is real, from 0 to infinity including 0. We complete this proof using the epsilon delta definition of continuity of a function at a point. To do this, we simply take an epsilon greater than 0 and an arbitrary point c from our domain, then go through the motions of finding a delta greater than 0 so that any x in D that is within delta of c has an image within epsilon of c's image. However, our approach will actually force c into the denominator in our proof, so we will need to take care of continuity at 0 separately. Let me know if there are more epsilon delta continuity proofs you want to see! #RealAnalysis

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