Under your module imports, paste the following definitions: (define WIDTH 300) (define HEIGHT 160) (define ES (empty-scene WIDTH HEIGHT)) (define (next-size s) (/ s 2)) Next, write a tail-call recursive function called circles. This function should take two numbers, x and size, and a Scene scn. If size is less-than or equal to 2, then your function returns the scn unchanged (base case). Otherwise, your function should place a circle in the Scene that results from a recursive call to circles with x shifted by (+ size (next-size size)), a new size of (next-size size), and using the original Scene. After evaluating (circles 100 48 ES), your function should output this image of five blue circles, in this order, with the first circle at (x,y) coordinate position (100, 80):

Objective: Practice writing recursive functions in python3  Make the five recursive functions described below in python3 by using the starter code recursive_functions.py. For each function, figure out how to solve it conceptually : write down the base case (when recursion stops) and how each recursive function-call moves towards the base case. The functions should not print anything (except you may add temporary print statements to help debug them). You can test your program by using the provided program test_recursive_functions.py. Don't edit the test program. Put it into the same directory (folder) with your recursive_functions.py and run it. It will import your functions as a module, test your functions, and tell you when each function is returning correct results. 1. Factorial In math, if you have a number n, the factorial function (written n!) computes n x (n-1) x (n-2) x (n-3) x ... x 1. For example: 0! is defined to be 1 1! = 1 2! = 2 x 1=2 3! = 3 x 2 x 1=6 4! = 4 x 3…

Write code to complete raise_to_power(). Note: This example is for practicing recursion; a non-recursive function, or using the built-in function math.pow(), would be more common.Sample output with inputs: 4 24^2 = 16 def raise_to_power(base_val, exponent_val):   if exponent_val == 0:      result_val = 1   else:      result_val = base_val * ''' Your solution goes here '''    return result_val user_base = int(input())user_exponent = int(input()) print('{}^{} = {}'.format(user_base, user_exponent,      raise_to_power(user_base, user_exponent)))

PYTHON Code your own Python function to solve Ax=b. Add a documentation string section to be used with the Python function help() function. Demonstrate the function is correctly implemented, and explain your testing approach.

Below, enter code to complete implementation of a recursive function palindrome() that determines whether an input string is a palindrome or not: 3. palindrome(s):

Please answer quickly in python