EDB — 29P

6.5 Upper and lower limits[29P]

From the previous definition we move on to the definitions of “limit superior” \(\limsup \) and “limit inferior” \(\liminf \). The idea is so expressed.

In particular, defining \(l=\limsup _{x→ x_ 0} f(x) \), the previous formulas characterize exactly the "limsup". We make them explicit further in what follows. (It is recommended to try to rewrite autonomously some items, by way of exercise).

Exercises

1. [0BP]↺↻

2. [0BQ]↺↻

3. [29R]↺↻

4. [29S]↺↻

5. [29T]↺↻

Other exercises on limits of sequences can be found in Sec. [0CN]↺↻.