Recursive Power Function Write a function that uses recursion to raise a number to a power. The function should accept two arguments: the number to be raised and the exponent. Assume that the exponent is a nonnegative integer. Demonstrate the function in a program.

Python 6. Sum of Numbers Design a function that accepts an integer argument and returns the sum of all the integers from 1 up to the number passed as an argument. For example, if 50 is passed as an argument, the function will return the sum of 1, 2, 3, 4, ...50. Use recursion to calculate • the sum.

C Programming Language Note: Input and Output Must be the same Write in C Language

PYTHON Problem Statement Given a list of numbers (nums), for each element in nums, calculate how many numbers in the list are smaller than it. Write a function that does the calculation and returns the result (as a list). For example, if you are given [6,5,4,8], your function should return [2, 1, 0, 3] because there are two numbers less than 6, one number less than 5, zero numbers less than 4, and three numbers less than 8. Sample Input smaller_than_current([6,5,4,8]) Sample Output [2, 1, 0, 3]

C++ The binary search algorithm given in this chapter is nonrecursive. Write and implement a recursive version of the binary search algorithm. The program should prompt Y / y to continue searching and N / n to discontinue. If an item is found in the list display the following message: x found at position y else: x is not in the list Use the following list of integers when testing your program: 2, 6, 8, 13, 25, 33, 39, 42, 53, 58, 61, 68, 71, 84, 97

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MULTIPLE FUNCTIONS AND RECURSIVE FUNCTIONS HANDS-ON use #include<stdio.h>

Python question Analysis: Invariants (Q16-17) For each of the following functions, identify the loop invariant, exit condition and post condition.    Question 16 (Invariant 1) This function returns the list of integers that are multiples of both 3 and 7 that occurs within a given list. Identify the loop exit condition, the loop post-condition, and the loop invariant at the end of the loop, which shows the algorithm’s correctness. def multiples_count(lst):    """    Input: a list of integers, lst    Output: the list of integers in lst that are multiples of both 3 and 7    """    res = []    for i in range(len(lst)):        if lst[i]%3 == 0 and lst[i]%7 == 0:            res.append(lst[i])        # Identify the loop invariant here    return res Question 17 (Invariant 2) This function checks if a given list (of comparable elements) is sorted in ascending order. Identify the loop exit condition, the loop post-condition, and the loop invariant at the end of each iteration of the loop, which…

17: recursion.cpp) Write two recursive integer functions. The first function should calculate factorials using the definition 0! = 1 and n! = (n-1)! x n. In addition, if n is too large it should be able to detect integer overflow before it happens. The next function should calculate the greatest common factor (gcf) of two numbers. If the second number is zero, then the gcf is the other number. Otherwise, the gcf of a and b is the same as the gcf of b and a mod b.