Limits
Table of Contents
1. Formal Definition
The limit, \( L \), of a function \( f(x) \), as \( x \) approaches some \( a \) is defined as:
\[ \forall \epsilon > 0, \ \exists \delta > 0, \ s.t. | f(x) - L | < \epsilon \] \[ \forall x \in (a - \delta, a + \delta) \]
The notation for this is \( \lim_{x \to a} f(x) = L \)
2. Example
2.1. Example 1
Show that: \( \lim_{x \to 2} (x^2) = 4\)