Equations that satisfy requested properties

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SUMMARY

The discussion focuses on finding equations that meet specific properties: a continuous and bounded function f:(0,infinity) -> R without global extrema, and a continuous function k:[0,infinity) -> R also lacking global extrema. Participants suggest using trigonometric functions as potential solutions, particularly emphasizing the combination of monotonic functions for the first equation. The conversation references a related thread for further insights.

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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.
 
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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).
 

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