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big-oh relationship

The following is a big-oh relationship:

n^10 is O(3^n)

Please give witnesses n0 and c that can be used to prove the relationship. Choose your witnesses to be minimal, in the sense that n0-1 and c are not witnesses, and if d < c, then n0 and d are not witnesses.

As a side note to the problem -- it may not be clear what d represents. d represents any positive constant that any function T(n) is O(dT(n)), regardless of whether d is a large number or a very small fraction, as long as d > 0. Typically it is used in the context of showing that constant factors do not matter.

Solution Summary

The big-oh relationship is shown.

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