This discussion of pathology is interesting to me. And long overdue, I think. I deliberately expose students to the inherent weaknesses of their machines.
I agree with Jerry that we tear down learning by deliberately laying down pathological examples as unmarked land mines. I doubt that these sorts of bizarre functions occur in the real world.
But, shouldn't students be struck with something like integral(0,10000,e^(-x^2),x) = 0. Go ahead, try it on your favorite numerical integrator. Try graphing sin(47x) (or something similar, depending on screen resolution) ... Try to find a point of intersection of y1=sin(x) / x and y2 = 1/x on a TI-8x. Drat, no sign change...
Is there something to *teach* by looking at these sorts of examples (if that is our honestly stated, up front intent)? I think so. And, remarkably, many of my own students are *interested* in seeing their machine screw up! And want to know *why* it happened.