# Math Help - sampling a smooth function

1. ## sampling a smooth function

Hi everybody,

First, I am sorry if it is not the right place to ask my question. Could someone please help me with the following question:

After sampling a smooth function (or at least a continuously differentiable function) like f(.) with a small enough sampling time, is it a correct assumption to say that f(n+1) (sample at (n+1)th instant) is approximately equal to f(n) (sample at nth instant)? is there any theorem in this respect? Thank you very much for your kind help.

2. ## Understanding

Can we have an example please?

I think what you are asking is given a function $f$ that it differentiable at $x=a$ and a maximum discrepancy $\delta>0$, find a corresponding $\epsilon>0$ such that $|f(a+\epsilon)-f(a)|<\delta$, and yes, this will always be the case, but it will be different for each function and $\delta$.