One day I was amusing myself with HP graphic calculator in typed the following function:
y = x exp(sin x)
Calculator showed function with strange route. Irrespective of how tiny part of x axis I examined (for ex. 1.10-15 to 2.10-15), there was huge amount of peaks, going from almost zero to 1.10+6 or more.
What kind of function is this? Has anything to do with fractals? Bear in mind that I'm a biochemist, not mathematician.

Try this one:

y = sin(1/x)

!!!
Yep, that would look pretty hairy as x approaches zero :)
Kind of boring for x > 1, though.

One day I was amusing myself with HP graphic calculator in typed the following function:
y = x exp(sin x)


Are you sure this is the function you graphed? This will be quite well behaved, even near 0. The x part nicely approaches 0 and the exp(sin x ) nicely approaches 1, so the whole thing goes to 0.

Plot of x*e^sin(x) should not be weird.

sin(x) is a sine wave, varying from zero to plus one, then to zero, then to minus, & back to zero. It repeats with period 2Pi

e^sin(x) looks a bit like a sine wave. Minimum is approximately .368 when sin(x) = -1 Maximum is e (approximately 2.718), when sin(x) = +1Multiplying the above sine-wave like function by x results in an oscillating graph with recurring maximums & minimums. As x increases, each minimum is larger than the previous minimum; Each maximum is larger than the preceding maximum.

The curve should be continuous. When I plotted it using MathCad, it seemed well behaved. As x grows without bound, both the maximums and minimums also grow without bound.

Sorry, I made mistake. I meant this function:
y = x exp(sin(1/x))