Average velocity and instantaneous velocity In some books of Physics in Italian language, they write that the instantaneous velocity $v$, is:
$$v=\frac{dr}{dt}=\lim_{\Delta t \to 0} \frac{\Delta r}{\Delta t}$$
where $v_{\text{avg}}={\Delta r}/{\Delta t}$, is measured by a speedometer (tachymeter) of a car. It is correct to affirm that: the velocity measured by a tachymeter is the instantaneous velocity?
For my humble opinion this affirmation is a false because not exists a precise instrument, that is always subject to errors and it not can never measure an instantaneous velocity. 
 A: For all practical purposes, it is the instantaneous velocity. All tools have an error. Let me pose a question: if you see an object move, do you see its instantaneous velocity at the current moment or its velocity a fraction of a millisecond ago, since it takes time for the light to hit your eyes?
Any tool for these type of measurements works by taking the average in a small fraction of time. This explains the $\Delta t \to 0$, as opposed to $\Delta t = 0$. There is nothing that will measure over a period of no time - then the expression would be irrational, dividing by $0$. But $\Delta t$ does approach $0$, though it never reaches it. This means that for all purposes, it is instantenous - this is the power of calculus.
A: The strict answer is that the speedometers on modern cars show a rolling average gauged over a short time period, and not a truly instantaneous speed. The display is determined by the rate at which sensors pick up the rotary motion of the car's wheels, which is done on a sampling basis, with a definite time lag (albeit a short one) between the samples. Usually the display includes a damping factor to prevent rapid small changes to the displayed speed. 
