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...
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...
17 April 2020
"And I shall put discontinuity in thy domain"
I recently noticed on Youtube a solution to an indefinite integral that I think is a useful chance to clarify an important point about antidifferentiation of a given...
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...
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...