Timeline for Why do we teach calculus students the derivative as a limit?
Current License: CC BY-SA 2.5
4 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Oct 6, 2012 at 2:10 | comment | added | user21349 | This example can be done straightforwardly without limits, using infinitesimals (either informally or in NSA). | |
| Apr 3, 2011 at 23:08 | comment | added | Toby Bartels | For the more general example, one should also ask that $f$ is not differentiable at $0$. (By varying such $f$, we can get any derivative at all, or none. Taking $f(x) = x \sin(1/x)$, extended continuously, gives a very interesting example that's come up elsewhere on this page.) | |
| Sep 27, 2010 at 17:12 | comment | added | Igor Belegradek | If you want example with nonzero derivative consider $x|x|+x$. | |
| Sep 27, 2010 at 15:33 | history | answered | Igor Belegradek | CC BY-SA 2.5 |