To determine which sequences can be approximated by \(4n^3\), we need to look for sequences that grow at a similar rate as \(4n^3\) as \(n\) becomes large. Generally, sequences with leading polynomial terms of degree 3 can be compared to \(4n^3\).
If you have specific sequences in mind, you can provide them, and I can help analyze those. In general, though, sequences of the form:
- \(an^3\) for any constant \(a\) (where \(a \approx 4\))
- \(an^3 + bn^2 + cn + d\) as \(n\) grows large, can also be approximated by \(4n^3\) since the \(n^3\) term will dominate.
On the other hand, linear sequences \(O(n)\), quadratic sequences \(O(n^2)\), or exponential sequences \(O(a^n)\) will not be well approximated by \(4n^3\).
If you can provide specific examples or options, I can give a more precise answer!
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