5) The code below returns the number of zeros at the end of n! (factorial n] int zeros (int n) int res = 0; while (n!=0) res n /= += n/5; 5; return res; Rewrite this method recursively: 6. Write a recursive function that returns the product of the digits of its integer input parameter, n. You omay assume that n is non-negative. For example, productDigits (243) should retum 24. since 2 x 4x3 = 24. int product Digits (int n) { 7. Let us define the weighted sum of an integer array a[0], a[1], a[2], ..., a[n-1] be a[0]*1 + a[1]*2+ a[2]*3 + .+a[n-1]*n. For example, the weighted sum of the array(5,2,6] would be 5*1+2*2+6*3 = 27. Write a recursive function that takes in an array numbers and its length n, and returns its weighter sum. You can assume n is non-negative integer. int weightedSum(int numbers [], int n) { 8. Mathematically, given a function f, we recursively define fin) as follows: if k= 1, f'(n) = f(n). Otherwise, for k > 1, f(n) = f(f(n)). Assume that there is an existing function f, which takes in a single integer and returns an integer. Write a recursive function fcomp, which takes in both n and k (k > 0), and returns f(n). int fint n); int fcomplint n, int k){ 9. What would be the value of fun(7) for the following function? int fun(int x) if(x==0) return; if(x3 ==0) return fun(x/3); return fun(x-1) + X; 10. Draw the recursion tree to find out the value of f(5) int fint n) int ans; int i; if(n