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The Formal Version Exercises

Example 1

For the given continuous function, value of c, and ε, what is f(c) and an appropriate δ that will guarantee the continuity of f?

5x – 2 , c = 3 , and ε = 1.

Example 2

For the given continuous function, value of c, and ε, find f(c) and a value of δ such that if |xc| < δ, |f(x) – f(c)| < ε.

ex , c = 0 , and ε = 1.

Example 3

For the given continuous function, value of c, and ε, what is f(c) and a value of δ guaranteed by the continuity of f?

x2 + 2 , c = -2 , and ε = 0.2.