Complete the code that returns the value of f(x), which has the value 1 inside the range –1 < x <1 otherwise it is the value 0. { 1, x€ [-1,1] 0, otherwise f(x) = # complete the function to return the value of f(x) given x. # return as the value called variable "fval" def function_f(x): # your code here return fval

ASSIGNMENT: Write a program to use the capability of Recursion to calculate factorials. For example, 5 factorial is normally written as 5! 5! = 5*4*3*2*1 5! = 120 Use recursive function calling to multiply. 5*4*3*2*1 And then print the result. 120 Your output should resemble the image below. >sh -c jav d. -type f > java -cla 5 4 2 5! = 120 } Note: 5! is use in this example but your program should calculate the factorial for any number entered.

Sum of two squares def sum_of_two_squares(n): Some positive integers can be expressed as a sum of two squares of some positive integers greater than zero. For example, 74 = 49 + 25 = 7^2 + 5^2. This function should find and return a tuple of two positive integers whose squares together add up to n, or return None if the parameter n cannot be broken into a sum of two squares.To facilitate the automated testing, the returned tuple must present the larger of its two numbers first. Furthermore, if some integer can be broken down to a sum of squares in several ways, return the breakdown that maximizes the larger number. For example, the number 85 allows two such representations 7^2 + 6^2 and 9^2 + 2^2 , of which this function must return (9, 2).The technique of two approaching indices that start from the beginning and end of a sequence, respectively, and approach each other until they meet somewhere is directly applicable to this problem. In this problem, these indices crawl towards each…

Complete the function that calculates the sum of the first n+1 terms of the geometric series a, ar, ar² ar³, arª ….. arn Note that the series begins with a and the last term is ar", in total there are n+1 terms. 1: # complete the function given the #variables a,r,n and return the value as series_sum. def sum geometric_series(a,r,n): # YOUR CODE HERE return series_sum print (sum_geometric_series (4.0, 5, 10))