Please solve problem 7?This is my answer Please solve problem 7?This is my answe
ID: 3739246 • Letter: P
Question
Please solve problem 7?This is my answer Please solve problem 7?This is my answer1/n, 2^10, lognloglogn, (logn)^2 , 2^logn , n/logn , 4^2*n , 2^4*n, 6nlogn+2n, n-n^3+6n^5, 3n +logn^100, n! , (3/2)^n, 2^n, n^n
Hint, just plug 10^6 to compare everyone, Becasue 10^6 is enough to test, I am not sure this is ok, just check that ? Lined Lise 1 Se CSCE 235-Dsr Java the Ays (a) Prove, using the definition that f(n) E 0(n"). (b) Prove, using the limit method that f(n) E (n3) 6. 6 points Let f(n) - aoe be an exponential function where ao R and e> 1 and let g(n)bd also be an exponential function where bo ER+ and d c (a) Prove, using the definition that f(n) E O(g(n)). (b) Prove, using the limit method that f(n) E O(g(n Survey of elementary 7. 9 points Order the following functions in increasing order of growth and indicate asymptotic equiva- s that are ? of each other). You need not give a formal proof for each. This is one help Cet Sign n By signing in gre list, not three. ???? ???"n?? ???, ??ME3? og(n), 1,20,6n log (n) 2log (n), 2". 24n,4%, 3n + log (nen'), log (n) log log (n) 8. 5 points composite input : An intunger output: true if n is prime, false otherwise for k-2,., Vn do Consider the following algorithm that computes whether or not a given integer a is prime or QQea,??? AMR if n mod k-0 then output false end end output true;
Explanation / Answer
Solution:
1/n, 2^10, log log n, log(n) log logn, (logn)^2 , n/logn , 2^log n , 3n +logn^100, 4^2*n , 2^4*n, 6n logn+2n, n-n^3+6n^5, (3/2)^n, 2^n, n! , n^n
The correct order is given above the bold functions are the one which needed to be replaced, else all is fone.
Explanation:
2^ log n can also be written as 2^log 2 (This is logarithmic property)= n (considering log of base 2)
log a^b can also be written as b log a
that is why 3n + log(n^100) = 3n + 100 log n
n! is close to n^n but smaller, according to string's approximation.
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