Number 3 +4n + 8 is O(n). 3. Give a formal proof that f(n) 5m3 +3n2...
Example 3: The Growth of Functionsand Asymptotic notation a) Show that x is O(x )but that r is not O(x b) Give as good a big-O estimate as possible for each of the following (A formal proof is not required, but give your reasoning): log,n! 7n n +nlo 3n2 +2n+4 . (n log, (log,n") 2 42" c) Which of the functions in part b) above has the fastest growth rate? d) Show that if f(x) is Ollog, x)where b>1, and...
1. a) Let f(n) = 6n2 - 100n + 44 and g(n) = 0.5n3 . Prove that f(n) = O(g(n)) using the definition of Big-O notation. (You need to find constants c and n0). b) Let f(n) = 3n2 + n and g(n) = 2n2 . Use the definition of big-O notation to prove that f(n) = O(g(n)) (you need to find constants c and n0) and g(n) = O(f(n)) (you need to find constants c and n0). Conclude that...
For each pair of functions determine if f(n) ? ?(g(n)) or f(n) ? ?(g(n)) or f(n) ? O(g(n)) and provide a proof as specified. For each of the following, give a proof using the definitions. 1. f(n) = log(n), g(n) = log(n + 1) 2. f(n) = n3 + nlog(n) ? n, g(n) = n4 + n 3. f(n) = log(n!), g(n) = nlog(n) 4. f(n) = log3(n), g(n) = log2(n) 5. f(n) = log(n), g(n) = log(log(n))
3. Evaluate each of the following limits. 4n? - n +5 (a) an = (-1)","; (b) an= n+1 3n2+1 n n+1 (c) an= 5n (d) ann +1 n 3n (e) an=- () 4n = 5 - n+1 1.1" (g) an= (h) an= (-1)" 2 - 1 n
Make this program using MATLAB AND SHOW THE DETAIL WORKING n2 if n 10 2. Let f(n)3n2 2 if 10 n < 30 4n if n 2 30 Create an m-fhle with a program to find the sum 50 Σ f(n). n=1 Hint: You may find the following commands to be useful: for elseif else end if When you are done, run your program and write the value of the sum here: 50 f(n) Even if you do not manage...
Give a good big-Oh characterization in terms of n of the running time of the following. Provide brief justification for your answer (in terms of finding a k and n_0). 4n^5 + 3n^3 + 7 15n^12 + 3n log n + 2n 3n log n + 2log n + n 12n*3^n + 50n
2. Asymptotic Notation (8 points) Show the following using the definitions of O, Ω, and Θ. (1) (2 points) 2n 3 + n 2 + 4 ∈ Θ(n 3 ) (2) (2 points) 3n 4 − 9n 2 + 4n ∈ Θ(n 4 ) (Hint: careful with the negative number) (3) (4 points) Suppose f(n) ∈ O(g1(n)) and f(n) ∈ O(g2(n)). Which of the following are true? Justify your answers using the definition of O. Give a counter example if...
Simplify each expression. Thanks 4n 6 n-3 2n 7) a+4_6 2a +6 2 8) 9) x+5 x +3 10) 6 r-6 r+ 3
Consider the two reactions. 2 NH,(g) + 3 N, O(g) - 4N, (g) + 3H,O(1) 4NH,(g) + 30,(g) — 2N, (g) + 6H, 0(1) AH = -1010 KJ AH = 1531 kJ Using these two reactions, calculate and enter the enthalpy change for the reaction below. N,(g) + 40,(8) NO(g) AH- AHL