For the given continuous function, value of c, and ε, find f(c) and an appropriate δ as guaranteed by the continuity of f.
5x - 2 , c = 3 , δ = 1
Answer
Since c = 3,
f(c) = f(3) = 5(3) - 2 = 13.
We're given ε = 1.Subtract c from all parts of the inequality and find δ.Subtracting c = 3, we find
-0.2 < x - 3 < 0.2
so δ = 0.2.