Answer: Limit of Big-O Terms: O(1/x) & O(x)

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SUMMARY

The limits of big-O terms O(1/x) and O(x) as x approaches 0 are definitively established. The limit of O(1/x) approaches infinity as x approaches 0, while the limit of O(x) approaches 0. The capital O notation indicates that O(1/x) behaves like 1/x, confirming its behavior towards infinity, and O(x) behaves like x, confirming its behavior towards zero.

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Avichal
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I'm a bit confused with limits of big-O terms. What should be the answer for following:-
1) limit of O(1/x) as x->0. O(1) maybe but I'm not sure.
2) limit of O(x) as x-> 0. O(1) or 0?
 
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The capital O symbol means that you quantity "behaves" like some other quantity in a certain limit. So, [itex]O(1/x)[/itex] behaves as [itex]1/x[/itex] and therefore goes to infinity as x approaches 0. For the same reason [itex]O(x)\to 0[/itex] as x approaches 0.
 

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