Problem 2 2.1) Show that (you need to show that the error term is O(h²)). f'(x) = − f(x+2h)+4ƒ(x + h) −3f(x) +0(h²) 2h 1 2.2) Let fƒ(x) = xe. Use the formula in 4.1) to find the "first" derivative of f(x) and plot the first derivative for x = [0, 1]. Pick appropriate value for h. 1 2.3) Let f(x) 1 =xe*. Use the formula in 4.2) to find the "second" derivative of f(x) and plot the second derivative for 2 € [0,1]

Given a long string use recursion to traverse the string and replace every vowel (A,E,I,O,U) with an @ sign. You cannot change the method header. public String encodeVowels(String s){ // Your code here }

6. Code for implement insertion sort in java.

def findOccurrences(s, ch):     lst = []     for i in range(0, len(s)):         if a==s[i]:             lst.append(i)     return lst Use the code above instead of enumerate in the code posted below. n=int(input("Number of rounds of Hangman to be played:")) for i in range(0,n):     word = input("welcome!")     guesses = ''     turns = int(input("Enter the number of failed attempts allowed:")) def hangman(word):            secrete_word = "-" * len(word)     print(" the secrete word " + secrete_word)         user_input = input("Guess a letter: ")         if user_input in word:         occurences = findOccurrences(word, user_input)         for index in occurences:             secrete_word = secrete_word[:index] + user_input + secrete_word[index + 1:]         print(secrete_word)     else:         user_input = input("Sorry that letter was not found, please try again: ")   def findOccurrences(s, ch):     return [i for i, letter in enumerate(s) if letter == ch]  *** enumerate not discussed in…