2. (15p) We shall consider a function A, defined by the recurrences A(0,n n+1 for n...
Just need help finding the A(3, n) general formula. A(1, n) = n + 1 and A(2, n) = 2n + 3 We shall consider a function A, defined by the recurrences 2. (15p) for n2 0 for m > 0 A(0,n+1 A(m,0-A(m-1,1) A(m,-A(m -1, A(m, n -1)) for m,n > 0 Observe that A(1,A(0, A(1,) A(0,2)3 A(1,2A(0, A(1) A(0,3)4 and it is now not hard to see (as can be proved by an easy induction) that A(1,n) = n...
1. (Induction.) Consider the following program, called Ackbar(m,n). It takes in as input any two natural numbers m, n, and does the following: (i) If m-0, Ackbar(0, n) = n + 1. (ii) If n-0, Ackbar(rn,0) is equal to Ackbar(m-1, 1). iii) Otherwise, if n, m > 0, then Ackbar(m, n) can be found by calculating Ackbar(m - 1, Ackbar(m,n 1)) Here's a handful of calculations to illustrate this definition: Ackbar(1,0)-Ackbar(0,1) = 1 + 1-2 Ackbar (1, 1) Ackbar (0,...
[Partial Orders - Six Easy Pieces] A binary relation is R is said to be antisymmetric if (x,y) ER & (y,x) ER = x=y. For example, the relations on the set of numbers is antisymmetric. Next, R is a partial order if it is reflexive, antisymmetric and transitive. Here are several problems about partial orders. (a) Let Ss{a,b} be a set of strings. Let w denote the length of the string w, i.e. the number of occurrences of letters (a...
ſcos (n =)drdy - 2 sini where D is defined by x+y=1 Calculate the values of the following areas: 5. The part of the plane 3x+4y+6z=12 directly above the rectangle D, the four vertices of D are: (0,0), (2,0), (2,1) and (0,1) Answer: (761)/3 6. The part of the curved surface z=v(4-y^2) directly above the rectangle D, the four vertices of D are: (1,0), (2,0), (2,1) and (1,1) Answer: 1/3 7. The finite part of parabola z=x^2+y^2 cut by plane...
The Ackermann function is usually defined as follows: In+1 A(m, n) = {Am - 1,1) ( Alm – 1, A(m, n - 1)) if m =0 if m >0 and n=0 if m >0 and n > 0. Use the definition of the Ackermann function to find Ack(3,2). Please show your work step by step.
2.1(9pts) Consider thc following contour plot for thc arbitrary function f(x,y): Y 0 2 Х -1 + 1. What is vf(0,0). Why? 2. At the point (0,2), in what direction should one move to increase the fastest? 3. Which vector has the greater magnitude: Vf(-1,0) or f(2,0)? CS Scanned with CamScanner
Type or paste question here 3. (20 pts.) Consider the function f defined on (0, 2) by 2+1 f(x) = = { 0<x< 1 1<x< 2 (a) Denote by fs the sum of the sine Fourier series of f (on (0,2]). Plot the graph of the function fs for x € (-2, 4), indicating the values at each point in that interval. Compute fs(0) and fs(2). [You do not have to compute the coefficients of the Fourier series.] (b) Denote...
Question 2 (2.5 points) Longest common subsequence Consider the procedure to determine the length of the longest common subsequence, LCS- LENGTH(X, Y). It solves the LCS problem in a bottom-up manner, by filling out a 2-D tabular LCS-LENGTH(X, Y) m = X.length 2. n-Y.length 3. let cO.m, 0n] be a new array 4, for i = 0 to m for/ = 0 to n else if ATY ci,ci ,j-1 +1 10 else 12. return clm, n] For example, X (B,...
that AB- 100 1 2 20 2 2 0 and trices shown to the right e A be the oorresponding n ×n matrix and let B be i s in ers e Guess the to m or B, and then st Use the algorithm for finding A to find the invers s of the 3 330 3 330 4444] 11 1[10 If A is the corresponding n× n matrix and B is its inverse, which of the following is B?...
How would you use this stored procedure to change the price of any copy of book 0180 whose format is paperback to $10.95? using MYSQL 8.0 Command line Client This is the database script for the homework above CREATE DATABASE HENRY; USE HENRY; CREATE TABLE AUTHOR (AUTHOR_NUM DECIMAL(2,0) PRIMARY KEY, AUTHOR_LAST CHAR(12), AUTHOR_FIRST CHAR(10) ); CREATE TABLE BOOK (BOOK_CODE CHAR(4) PRIMARY KEY, TITLE CHAR(40), PUBLISHER_CODE CHAR(3), TYPE CHAR(3), PRICE DECIMAL(4,2), PAPERBACK CHAR(1) ); CREATE TABLE BRANCH (BRANCH_NUM DECIMAL(2,0) PRIMARY KEY,...