(1 point) [3 Marks] Note that 0 € N. Give a recursive function f: N N...
(1 point) (3 Marks] Note that 0 € N. Give a recursive function f:N → N that represents the sequence ao, 21, 22, az... if an 10n + 1. (1 point) [3 Marks] Find mod(31004 + 1004!, 11). A. I am finished this question
(1 point) [3 Marks] Note that 0 € N. Give a recursive function f:N + N that represents the sequence ao, 21, 22, az... if an = 10n + 1.
Note that 0 EN Give a recursive function f:N → N that represents the sequence ao, 21, 22, 23... if an 10n +1.
3. The sequence (Fn) of Fibonacci numbers is defined by the recursive relation Fn+2 Fn+1+ F for all n E N and with Fi = F2= 1. to find a recursive relation for the sequence of ratios (a) Use the recursive relation for (F) Fn+ Fn an Hint: Divide by Fn+1 N (b) Show by induction that an 1 for all n (c) Given that the limit l = lim,0 an exists (so you do not need to prove that...
2. Which of the following recursive functions, written in a fictitious language, are tail recursive? Select all that are A. function f(n) ifn<2 else f(n-1) + f(n-2) end If m=0 else B. function g(m,n) g(m-1,m'n) C. function h(n) if n 100 else 3 h(n+5) end D. function j(m.n) IT m=n 100 j(m-n,n) 10 j(n,n-m) elseif mn else 2. Which of the following recursive functions, written in a fictitious language, are tail recursive? Select all that are A. function f(n) ifn
Question 3 (1 point) The function f is defined by the power series 1)2 3! 5! 72n+1)! 1)% n-0 (2n+1) ! for all real numbers x. Use the first and second derivative test by finding f(x) and f"(x). Determine whether f has a local maximum, a local minimum, or neither at x=0. Give a reason for your answer. Use the Question 3 (1 point) The function f is defined by the power series 1)2 3! 5! 72n+1)! 1)% n-0 (2n+1)...
Let Σ = {0, 1). (a) Give a recursive definition of Σ., the set of strings from the alphabet Σ. (b) Prove that for every n E N there are 2" strings of length n in '. (c) Give a recursive definition of I(s), the length of a string s E Σ For a bitstring s, let O(s) and I(s) be number of zeroes and ones, respectively, that occur in s. So for example if s = 01001, then 0(s)...
Problem 5. (1 point) [5 Marks] Consider the following integer n = 516734400 = 2 · 37 · 52 · 72 · 133. a) How many positive divisors does n have? b) How many of the positive divisors of n are perfect cubes? That is, the number can be written as (k)3 for some k e Z. c) How many of the positive divisors of n are relatively prime with 21? A. I am finished this question
|(a) Consider the following function for > 0 f (x)= = -4x 48x (i) Find the stationary point(s) of this function. (3 marks) (ii) Is this function convex or concave? Explain why. (3 marks) (iii What type of stationary point(s) have you found? Include your reasoning. (4 marks) |(b) Show that ln(a) - a has a global maximum and find the value of a > 0 that maximises it. Do the same for ln(a) - a" where n is a...
(14) Given a sequence of integers {fi,f2 /. defined by the following recursive function f (n)-., n e N such that s(2) 5, Evamine the sruture of this sequence and then compute J, in closed-form.Prove by using strong induction as discussed in class that your function f, is indeed correct.