[chiralSPO (OP)]

f(x) = lim    x^a     or just f(x) = x^∞
         a→∞

for –1 < x < 1, f(x) = 0
for x = 1, f(x) = 1
for 1 < x, f(x) = ∞ (unbounded, strictly positive)
for x = –1 f(x) = no f*n clue! (it's neither positive nor negative)
for x < –1 f(x) = no f*n clue! (it's completely divergent, neither positive nor negative)
I'm not sure if x

I'm sure ya'll can come up with some other poorly behaved functions

PS: I remember sin(1/x) is also a baddie when trying to get close to 0, but I think the above is worse.

[Bored chemist]

"Who can find a more poorly behaved function?"
Central government?

[chiralSPO (OP)]

"Who can find a more poorly behaved function?"
Central government?

Tell me about it!

[evan_au]

A nasty one to test student programs to find the roots of a function is:

y=e^-1/x2

This function has a root y=0 at x=0, but:
- It is a root of infinite degree, which means that root-finding functions will take forever to get there
- If/when the function finds the root, it blows up (unless you are using symbolic maths package of suitable sophistication).

[evan_au]

The Dirac Delta function is widely used in mathematics, physics and digital signal processing:

y=0 for x≠0
y=∞ for x=0
Area under the curve = 1

See: https://en.wikipedia.org/wiki/Dirac_delta_function

[chiralSPO (OP)]

y=e-1/x2

ooo baby! that IS nasty!

[evan_au]

How about the following mathematical equation?

Σn = 1+2+3+4+....+∞  = ^-1/₁₂

Apparently, it has application in string theory...