# Math Help - continuity proof

1. ## continuity proof

1)
Define f: R -> R by f(x) = x^2 - 3x + 5. Use the definition of continuity to prove that f is continuous at 2

2)
Prove or give a counterexample: Every sequence of real numbers is a continuous function

2. Originally Posted by slowcurv99
1)
Define f: R -> R by f(x) = x^2 - 3x + 5. Use the definition of continuity to prove that f is continuous at 2

2)
Prove or give a counterexample: Every sequence of real numbers is a continuous function
there are several definitions for continuity of a function, which are you using in class?

3. Let f: D->R and let c be an element of D. We say that f is continuous at c if for every e>0 there exists a q>0 such that |f(x) - f(c)| < e whenever |x-c| < q and x is an elemend of D.
If f si continuous at each point of a subset S of D, then f is said to be continuous on S. If f is continuous on its domain D, then f is said to be continuous

4. I have absolutely no idea what your question means.