Tag: continuity

5 January 2022
A bumpy ride
We take again inspiration from the Putnam competition, for an exercise on continuity and differentiability of real fuctions obtained by "stretching" a basic replica. Let...
Leggi di più - Read more
9 July 2020
Uneven integration
Very seldom does one need to make use of the actual definition of Riemann integral. Most of the times, in fact, we are dealing with very "regular" functions for which a whole...
Leggi di più - Read more
6 July 2019
Ups and downs
We are given a function \(f(x)\), for which the right derivative \[f'_+(x) = \lim_{h\rightarrow 0^+}\frac{f(x+h)-f(x)}{h}\] is defined in \(\Bbb R\). We also know...
Leggi di più - Read more
9 June 2019
Monotonically speaking
The concepts of monotonicity and continuity are very different. However, if we consider a monotonic function whose domain is an interval, we can deduce that right and left limits...
Leggi di più - Read more