Task 1: In this task, you will complete four recursive functions and trace them for some sample inputs. a. Create an HTML file that includes five buttons with the following labels: "recursive find A", "recursive find B", "recursive find C", "recursive palindrome", and "recursive count asterisks". Create a div in your HTML to hold the results of calls to corresponding javascript methods. You can style this page as you like. Feel free to use the HTML and CSS from prior labs as a template, if you like. b. Create a JavaScript file that responds to clicks of these buttons. All implementations should be recursive. a. Problem 1. Create an array of 30 random numbers that range between 1 and 100. Then, write a function that will receive a number from the user and determine if that number exists in the array or not. For instance, assume the array is: [2, 93, 14, 89, 12, 3, 81, 15, 14, 89, 52, 96, 71, 82, 5, 2, 41, 23, 52, 59, 44, 44, 88, 39, 49, 50, 97, 45, 48, 36] Now, assume the user enters 89, the program should output true. But, if the user enters 77, the program should output false. Approach: We will be implementing this method in two different ways. Both will be recursive. First, implement a method called findA(x,A), where x is the number we are looking for and A is an array. In the body of the function, compare x with the FIRST item that is in the array. If this first item is equal to X, return true. If not, remove the first item from A and call findA(x,A) on the revised list. If you call find on an empty list, you will want to return false. Writing any explicit loop in your code results a 0 for this question. Remember to provide pre- and post-conditions. How many recursive calls will you need to search the entire list? Next, copy the following trace table in your Word file and trace the input values to the function findA (x,A) for when A and x are initially [1, 6, 10, 14, 77, 82, 100] and 77, respectively. As a guideline, we have populated the tables with the values for the first 2 calls and the corresponding returned values for each of those calls. Note that in this example, the call numbers will be populated top down (i.e. time elapses from row x to row x+1) while returned values are populated bottom-up (i.e. the value in row x is returned before the value in rowx-1). You may want to use console.log to observe these values when you write your solution. call# A value returned to this call 1 77 [1, 6, 10, 14, 77, 82, 100] TRUE 2 77 [6, 10, 14, 77, 82, 100] TRUE