2. Write a function that multiplies a polynomial by a constant (or scalar). scale :: (Num a, Eq a) => a -> Poly a -> Poly a For example: > scale 2 (P [-1,0,1]) P [-2,e,2] > scale e (P [0,0,2]) P []

For input vector x, write a function to check whether there exists at most 5 elements in x whose values are less than 7.

Change two lines of code of:   def solution(A, K):     n = len(A)     for i in range(n - 1):         if (A[i] + 1 < A[i + 1]):             return False     if (A[0] != 1 and A[n - 1] != K):         return False     else:         return True   SO that it solves the question : you are given a implementation of a function def solution (A,K) This function, given a non-empty array A of N integers (sorted in non-decreasing order) and integer K, checks whether A contains numbers 1,2..K (every numbers from 1 to K at least once and no other numbers  (for example given array A, K=3 ; A(0)=1,  A(1)=1,  A(2)=2,  A(3)=3,  A(4)=3 then the function should return True  while for the following array A, K=2; A(0)=1,  A(1)=1,  A(2)=3  then the function should return False.) Assume that: -N and K are integers within the range (1....300,000) -each element of array A is an integer within the range (0...1,000,000,000) -array A is sorted in non-decreasing order

A university assigns student IDs of the form 1, 2, 3, ... such that if n students are currently enrolled, then the next student to enroll will receive and ID of n + 1. Consider the following algorithm that accomplishes this. // Global variable storing number of students currently enrolled current_student_count = 0 // Function that reads the above global variable, calculates new ID, and increments the global count assign_new_id(): count = current_student_count new_id = count + 1 current_student_count = count + 1 return new_id (a) If two different threads run the above code in parallel to enroll two different students, it is possible for the two students to receive the same ID, and for the current_student_count to have a wrong value. Explain how this is possible. (b) Modify the code above so that the problem in (a) does not happen.

Example 2: Let f and g be functions from the set of integers to the set of integers defined by f (x)= 2x+3 and g(x)= 3x+2. What is the composition of f and g, and also the composition of g and f?

Exercise 4B (1) Write a function which takes a list of the coefficients of a polynomial P(x) = ª₁ + ª₁x + a² + ….. +anxn of arbitrary degree n, and a value of x, and returns P(x). You can use the function given in lectures, ensuring you understand how it works. (2) Use the function to evaluate (a) P₁(x) = 4x4 + 3x² + 2 at x = 2. (b) P₂(x) = 2 — ¹x¹ at x = √√/2. Are these answers exact? Explain why or why not. (Use a print statements to show the evaluation of your function, and answer the question in a comment.) (3) The power series for the sine function sin(x) is given by ∞ x2n+1 (2n + 1)! sin(x) = Σ(−1)”. n=0 = x 6 + x5 120 for all x. Use the first four terms in this series in the Horner evaluation function at a suitable value of a to give an approximation of sin(π/4). (4) (a) Use your Horner's method function to evaluate the polynomial (x − 1)³ at the point x = 1.000001. (b) Is this answer correct? (c) Briefly explain why, or why not. (5) In week 3 we wrote a function to convert from…