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Solved: Give a big-O estimate for each of these functions.
Chapter 2, Problem 27E(choose chapter or problem)
Give a big-O estimate for each of these functions. For the function \(g\) in your estimate that \(f(x)\) is \(O(g(x))\), use a simple function \(g\) of the smallest order.
a) \(n \log \left(n^{2}+1\right)+n^{2} \log n\)
b) \((n \log n+1)^{2}+(\log n+1)\left(n^{2}+1\right)\)
c) \(n^{2^{n}}+n^{n^{2}}\)
Equation Transcription:
Text Transcription:
O
g
f(x)
O(g(x))
n log(n^2 + 1) + n^2 log n
(n log n + 1)^2 + (log n + 1) (n^2 + 1)
n^2^n + n^n^2
Questions & Answers
QUESTION:
Give a big-O estimate for each of these functions. For the function \(g\) in your estimate that \(f(x)\) is \(O(g(x))\), use a simple function \(g\) of the smallest order.
a) \(n \log \left(n^{2}+1\right)+n^{2} \log n\)
b) \((n \log n+1)^{2}+(\log n+1)\left(n^{2}+1\right)\)
c) \(n^{2^{n}}+n^{n^{2}}\)
Equation Transcription:
Text Transcription:
O
g
f(x)
O(g(x))
n log(n^2 + 1) + n^2 log n
(n log n + 1)^2 + (log n + 1) (n^2 + 1)
n^2^n + n^n^2
ANSWER:
Solution;
Step 1 :
The objective is to give the big-O estimate for the each of the following function.
(a)
Then
.’. The big-O estimate for .