Show that logn(na )= a
Euler-Maclaurin summation formula Using the Euler-Maclaurin summation formula, show that [ logn= xlogx - x - 41(x)logx+c+00), l<nex for some constant c, where w1(x) = {x} - 1/2. all x > 1 that My(x) = $* f60de+ſ*(0f'(dt-W1 (1)||1) – 4:1()f(x),
I understand how it was simplified to n^(∈/(sqrt(logn))), but I'm trying to understand how to prove that logn grows faster for 0<∈<1. The derivative seems too complicated to prove this via Lhopital's Rule, so I tried using WolframAlpha to compare the two with logn as the numerator: http://www.wolframalpha.com/input/?i=limit+as+n+approaches+infinity+(logn)%2F(n%5E(0.5%2F(sqrt(logn))))&rawformassumption=%7B%22FunClash%22,+%22log%22%7D+-%3E+%7B%22Log10%22%7D However, this gives me a result of 0 for any value above 0, which would mean that n^(∈/(sqrt(logn))) grows at a faster rate, even when 0<∈<1. When I try to graph it,...
Prove that the height of an AVL tree is bound by O(logn). and What is the least number of nodes in an AVL tree of height 25? (all work on both questions provided)
Order the following functions by growth rate: N, squrerootN, N1.5, N2, NlogN, N log logN, Nlog2N, Nlog(N2), 2/N,2N, 2N/2, 37, N2 logN, N3. Indicate which functions grow at the same rate.
7. A positive random variable Y is said to be a lognormal random variable, LOGN (u, 0), if In Y ~ N(No?). We assume that Y, LOGN (1,0%), i = 1,..., n are independent. [5] (a) Find the distribution of T = 11",Y. [4] (b) Find E(T) and Var(T) (5] (c) If we assume that M = ... = Hn and a = ... = 0, what does the the successive geometric average, lim (II",Y), converge in probability to? Justify...
11 QUESTION 11 What is the runtime of Binary Search? a. O(n) b. Onlogn) c. Of(logn)) d. Odlogn)
Determine convergence or divergence. n5 +1 n2(n/4) 1-e" logn coS_ 1n 1n
ind the approtade roin of analytlcidy fot eack complex fan.cfionse Logn. .of analy+icty far. .eac .CO +I
Please show the synthesis by not using Na, NH3 Not by ust
Sea Level Change (mm) Annual Lobbying on Oil and Gas ($mil) na na na na na na na na na na na na na na na na na na na na na na na na na na na na na na na na na na na na na na na na na na na na na na na na na na na na na na na na na na na na na na na na na na na na na...