Equations that satisfy requested properties

[tiki84626]

Homework Statement

Find the equations that satisfy the following properties:

1) f:(0,infinity) -> R is continuous and bounded, but f has no maximum and no minimum (that is global min and max).

2) k:[0,infinity) -> R is continuous, but k has no maximum and no minimum (again global min and max).

Homework Equations

The Attempt at a Solution

I'm thinking that i need to use a trig function for number 1, but beyond that I'm stumped.

 

[Dick]

Oh, come on. You can try harder than that. 1) is terribly easy. Find a continuous, bounded and monotone function on (0,infinity). A trig function will help for 2), but if you get a good example for 1) you can combine it with a trig function to get 2).

 

[LCKurtz]

This is a duplicate of this thread:

https://www.physicsforums.com/showpost.php?p=2562545&postcount=1

Please do not post the same question in different sections.