# 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*?

5*x *– 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 |*x* – *c*| < *δ*, |*f*(*x*) – *f*(*c*)| < *ε.*

*e*^{x} , *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*?

*x*^{2} + 2 , *c* = -2 , and *ε* = 0.2.