Question

What kind of discontinuity does f(x) = (x^3 - 3x^2 + 6 - 2x)/(x-3) have at x=3?

Answer 1

on first glance, one would say asymptotic discontinuity because the denominator is zero when you plug in x = 3

however, it it very likely that we can divide the numerator by x-3 and no longer have that "obvious" asymptotic at 3. i.e. it is most likely an illusion.

we have to divide before deciding

Answer 2

actually. what i'm describing seems more like a point discontinuity.

that is more likely the answer, deducted by the fact that f(3) = 0/0

Answer 3

okay describe a function with a jump discontinuity

Answer 4

not sure what you/they mean by describe.

i'm looking at this resource right now though. it's pretty good:

http://www.math.brown.edu/UTRA/discontinuities.html