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![- Write an algorithm which applies the bisection method to this
problem.
Return to the equation
-
sin² (x) + 1-2x = 0.
Write down the Newton method for this equation, that is,
In+1 = ?
Write a computer algorithm which implements the Newton method
from the previous step.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3088de2e-e8a1-46b2-ad91-8e46dd0ae125%2F098db38c-031d-4336-a8d4-e3c0dc755b83%2F0n9kt4_processed.jpeg&w=3840&q=75)
![• Suppose that we want to find a solution of the equation
sin² (2) + 1-2x = 0,
on the interval [0, π/2].
Is there a solution of the equation in this interval? How do you
know?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3088de2e-e8a1-46b2-ad91-8e46dd0ae125%2F098db38c-031d-4336-a8d4-e3c0dc755b83%2Fn1yts9_processed.jpeg&w=3840&q=75)
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- You are given a string of characters. Complete the below recursive method in JAVA or inPython to print the lowercase characters in a reverse manner and also print the count. Scontains the string, i is the starting index and c is the count, which are both initialized to0. [Note for Python Implementation: You are not allowed to use any built-in functionsexcept len(), print(), ord() and chr()]. def printReverse (s, i, c) : #To Do OR public void printReverse (String s, int i, int c) { // To Do } Sample Input Sample Output s = Axy3*8Gw57&Xyu1 count is 4, uwyxJava - Write an iterative method that calculates the SUM of all integers between 1 and a given integer N (input into the method). Write a corresponding recursive solution. (return answer, don’t print)Write a program that computes the following summation series using the Rational class:
- The factorial of a positive integer n —which we denote as n!—is the product of n and the factorial of n 1. The factorial of 0 is 1. Write two different recursive methods in Java that each return the factorial of n. Analyze your algorithm in Big-Oh notation and provide the appropriate analysis, ensuring that your program has a test class.You will be given an array A of length n. Write a method to calculate the following value of X using recursion. X = Ao x 7° + A1 x 7' + Az × 7² +. +An-1 x 7"-1 • The recursion can have any number of parameters. You can't use loops or math.pow() or a separate recursive function to calculate 7". The return type should be integer. • The range for n is 1Write a recursive algorithm with the following prototype: int divide (int x, int y); that returns x/y (integer division). You need not test for divide by 0. THE FUNCTION MUST BE RECURSIVE. (hint: base case should be when xGiven a list of integers, you want to know whether it is possible to divide the integers into two sets, so that the sums of the two sets are the same. Every integer must be in one set or the other. Write a recursive helper method that takes any number of arguments you like, and make the initial call to your recursive helper method from equalSum(). Do not use any loops or regular expressions. Test case 1: equalSum([2, 3, 5]) true Test case 2: equalSum([2, 2, 5]) falseStart with a pile of n stones and successively split a pile into two smaller piles until each pile has only one Each time a split happens, multiply the number of stones in each of the two smaller piles. (For example, if a pile has 15 stones and you split it into a pile of 7 and another pile of 8 stones, multiply 7 and 8.) The goal of this problem is to show that no matter how the pile of n stones are split, the sum of the products computed at each split is equal to n(n - 1)/2. Using strong mathematical induction, prove that no matter how the pile of n stones are split, the sum of the products computed at each split is equal to n(n - 1)/2.A very known application in natural language processing is to extract information from a given text. In this lab, you will be able to extract some emotions (Sad and Happy) from a given string and calculate the score of each emotion. You will be given below the words that express sadness, anger, and happiness. For each word, you will be given weight as well, so that when you are calculating for example the score for sadness in the text (string), you can use this formula:Write a recursive algorithm with the following prototype: int add (int x, int y); that returns x if y is 0; and adds x to y otherwise. THE FUNCTION MUST BE RECURSIVE. (hint: the base case should involve a test for y being 0; recursive case should reduce y towards 0)Write a recursive method to determine whether a String contains a 'q' not immediately followed by a 'u' (ignoring capitalization). In other words: • the word does contain at least one 'q' • and that q is followed by anything except a 'u' Carefully review the provided driver program to see example test cases. The method header is: public static boolean qNotFollowedByU(String word)use The C Programming Language Online Compile for Recamán's Sequence Implement this in a program. Write two functions, one for solving it iteratively, one for solving it recursively. Take two arguments from the command-line: an "i" or "r", and the term number (how many terms to print). Print out which method executed (was selected) and all the terms (and the number of terms).Recommended textbooks for youDatabase System ConceptsComputer ScienceISBN:9780078022159Author:Abraham Silberschatz Professor, Henry F. Korth, S. SudarshanPublisher:McGraw-Hill EducationStarting Out with Python (4th Edition)Computer ScienceISBN:9780134444321Author:Tony GaddisPublisher:PEARSONDigital Fundamentals (11th Edition)Computer ScienceISBN:9780132737968Author:Thomas L. FloydPublisher:PEARSONC How to Program (8th Edition)Computer ScienceISBN:9780133976892Author:Paul J. Deitel, Harvey DeitelPublisher:PEARSONDatabase Systems: Design, Implementation, & Manag…Computer ScienceISBN:9781337627900Author:Carlos Coronel, Steven MorrisPublisher:Cengage LearningProgrammable Logic ControllersComputer ScienceISBN:9780073373843Author:Frank D. PetruzellaPublisher:McGraw-Hill EducationDatabase System ConceptsComputer ScienceISBN:9780078022159Author:Abraham Silberschatz Professor, Henry F. Korth, S. SudarshanPublisher:McGraw-Hill EducationStarting Out with Python (4th Edition)Computer ScienceISBN:9780134444321Author:Tony GaddisPublisher:PEARSONDigital Fundamentals (11th Edition)Computer ScienceISBN:9780132737968Author:Thomas L. FloydPublisher:PEARSONC How to Program (8th Edition)Computer ScienceISBN:9780133976892Author:Paul J. Deitel, Harvey DeitelPublisher:PEARSONDatabase Systems: Design, Implementation, & Manag…Computer ScienceISBN:9781337627900Author:Carlos Coronel, Steven MorrisPublisher:Cengage LearningProgrammable Logic ControllersComputer ScienceISBN:9780073373843Author:Frank D. PetruzellaPublisher:McGraw-Hill Education