What is the time and space complexity (use big O notation) of this function? Answer briefly, not more than 2-3 lines.
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2) What is the time and space complexity (use big O notation) of this function? Answer briefly, not more than 2-3 lines.
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- 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…In mathematics, the triangle inequality states that for any triangle, the sum of the lengths of any two sides must be greater than or equal to the length of the remaining side. Write a function named, prg_question_1 to check whether three sides of given lengths would form a triangle or not. For example, for sides 12.5, 20.8, 15.0 your function must return true whereas for 4.8, 3.0, 12.0 it must return false as 4.8 + 3.0 is < 12. Do the following: 1. Follow UMPIRE process to get the algorithm. Write only the algorithm as code comments 2. Implement your function 3. Test your function for the sets of side lengths of units 10, 20, 15 and 4, 4, 10. Please follow the test criteria given in the code template