# Montonically increasing

• March 27th 2011, 12:25 PM
dwsmith
Montonically increasing
Just a general question.

Are all monotonically increasing functions divergent?
• March 27th 2011, 12:35 PM
skeeter
Quote:

Originally Posted by dwsmith
Just a general question.

Are all monotonically increasing functions divergent?

how about $y = \arctan{x}$ ?
• March 27th 2011, 12:37 PM
topsquark
Quote:

Originally Posted by dwsmith
Just a general question.

Are all monotonically increasing functions divergent?

In fact I just saw this function in another thread.

$f(x) = \frac{x}{|x| + 1}$

This is monotonically increasing, but $\displaystyle \lim_{x \to \pm \infty} = \pm 1$.

-Dan