I regularly choose a function for my numerical analysis class that looks bad (i.e., has jumps) when graphed on a small domain. For example,
plot(ln(1+x), x = -10^(-15) .. 10^(-15))
If I increase Digits or use a Taylor series to replace ln(1+x), the graph looks fine.
I tried this with cos(x) - x as follows:
plot(cos(x)-x, x = -10^(-16) .. 10^(-16))
(That's 10^-16, by the way.) I got what appears to be a jump discontinuity. However, I can't clear it up --- I've tried increasing Digits to 100, setting numpoints to 1000, setting adaptive to 50, and using a 50th degree Taylor polynomial in place of cos(x) - x.
Any ideas what's going on? (Is there a fix?)