Mathematics

Problem

The statement

\displaystyle \lim_{x\to 4} f(x)=9

is true for a differentiable function

f

. Describe precisely what this statement means in terms of two positive real numbers

\varepsilon

and

\delta

. In your explanation, address the following points: • the role of

\varepsilon

and what it measures, • the role of

\delta

and what it measures, • why the condition

x\neq 4

is included even though

x

is required to be close to

4