1a. Write a non-recursive function vowels() that accepts a character string and counts and returns the number of vowels (aeiou) in the string.

1b. Write a recursive function rvowels() that accepts a character string and counts and returns the number of vowels (aeiou) in the string. This solution should not include any loops. A global variable for the counter is acceptable. (Hint: one possible solution is to "chop" the string down until you are left with a single character.)

1c. Using the test string ‘this is a test to see if my program can accurately count the vowels' and the time operation described in the book on page 371 in the function timing, time the non-recursive solution and the recursive solution. Does this test provide any useable proof? Explain.

Place both your functions into one file. Dropbox your Word document showing all code and output, along with your Python file. In the Word document, include your answer to the above question: Does this test provide any useable proof? Explain.

2. Write a recursive function which accepts a string and its length and determines if the string is a palindrome. A palindrome is a string that reads the same frontwards and backwards. Hint: compare the first character with the last character. Equal or not? Go from there.