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Big O notation.
my bet would be n, 22n, n^2 log(n), 2*n^2, n^2*n;

a) 22n = O(n)
b) 2n2 = O(n) (or if it's 2^n * 2, then O(2^n), or if it's 2 * n^2, then O(n^2))
c) n2log(n) = O(n log(n)) (or if it's n^2 log (n), then O(n^2 log (n))
d) n = O(n)
e) n2n = O(n^2) (or if it's n^2 * n, then O(n^3)

log(n) = O(n^a) for any a > 0, so n * log (n) grows faster than n, but slower than n^2.

Any sort of exponential function grows faster than any power of n, so 2^n grows the fastest.

To encompass all possibilities, here is the order of growth in increasing order

n, 22n
n * log (n)
n^2, 2n^2
n^2 * log (n)
n^3
2^(n+1)

Your notation is atrocious.

Arrange the following growth rates in increasing order:
O (3n), O (n2), O (1), O (n log n)

Arrange the following growth rates in increasing order:
O (3n), O (n2), O (1), O (n log n)

Thanks , It's so much helpful for us.

Thank you.....

Ans for IGNOU Assignment MCS031 Question:7
1) O(1) - bounded function
2) O(3n) = O(n) - linear function
3) O(n log n) - when comparing n log n and n^2, note that log n is not bounded. However, any exponent of n grows faster than log n, so for some constant C > 0 and large enough n, log n <= C * n, and so n log n <= C * n^2 for some C > 0 and n > N for some N
4) O(n^2)

Arrange the following functions in increasing order of growth rate (with g(n) following f(n) in your list if and only if f(n)=O(g(n))).

a)n
b)10n
c)n1.5
d)2log⁡(n)
e)n5/3

10. Arrange the following growth rates in increasing order and justify your answer: O(n4), O(1), O(n3), O(nlogn), O( n2 logn), Ω( n2 logn), Ø(nlogn), Ø(n2), Ø(n15), Ω(n!).

O(1) < Q(n^1.5) < Q(nlogn) < O(nlogn) < Q(n^2) < omega(n!) < omega(n^2logn) < O(n^2logn) < O(n^3) < O(n^4)

for root values

Arrange the following growth rates in increasing order:
O ((23)n ) , O (n4), O (1), O (n 3log n)

Please help me for this question

Arrange the following growth rates in increasing order
O ((23)n ) , O (n4), O (1), O (n 3log n)

a. Arrange the following growth rates in increasing order
O((23)n ),O (n4),O(1),O(n 3log n)

Arrange the following growth rates in increasing order:
O ((23)n ) , O (n4), O (1), O (n 3log n)

Order the given functions by increasing growth rate.

f_1(n)=n^3f
1
​ (n)=n
3


f_2(n)=n^{0.3}f
2
​ (n)=n
0.3


f_3(n)=nf
3
​ (n)=n

f_4(n)=\sqrt{n}f
4
​ (n)=
n
​

f_5(n)=\frac{n^2}{\sqrt{n}}f
5
​ (n)=
n
​
n
2

​

f_6(n)=n^2f
6
​ (n)=n
2

Ghh

) Arrange the following functions into increasing order; that is, by asymptotic growth rate 2 ^ lg(lg(n)) + (sqrt(n)) ^ lg(n); 8 ^ lg(n); 0 ^ 0; (log n)!; 2 ^ lg(n); 3 ^ (2n) I log (n!); lg(2 ^ lg(lg(n))); lg((n + 10) ^ n); (1+2+3+***+n)

) Arrange the following functions into increasing order; that is, by asymptotic growth rate 2 ^ lg(lg(n)) + (sqrt(n)) ^ lg(n); 8 ^ lg(n); 0 ^ 0; (log n)!; 2 ^ lg(n); 3 ^ (2n) I log (n!); lg(2 ^ lg(lg(n))); lg((n + 10) ^ n); (1+2+3+***+n)

Arrange the following functions into increasing order growth rate :- O(n1/4), O(nl.5), O(n3lg n), O(nl.02), (n6), 2(n!), O(√n), O(n6/2), 22(2n)

Arrange the following functions in the increasing order of Growth rate

n, n!, n², sqrt(n), log n, nlogn, a" (where a is constant >1)