5. The growth of functions questions.A) True or False?• 3* is O (22n)TRUTHFALSE• If f(n) = 1 * 3 + 2 * 4 + 3 * 5+ ...n * (n + 2) thenf(n) is 0(n²)TRUTHFALSEB) Find Big-Theta the following functions. In your answer provide a simplestpossible function.In(3" * n")is e(.. .)n In(n² + 10") + n Innis O(.. .)• n lnn + In 2" + In(n!)is 0(. .)......

It is defined as the order of growth of the running time of an algorithm, it gives a simple…

Answered: 5. The growth of functions questions.…

Database System Concepts

7th Edition

ISBN:9780078022159

Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Chapter1: Introduction

Section: Chapter Questions

Problem 1PE

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Find the order of growth of the following sums. Use the ?(?(?))notation with the simplest function ?(?) possible. a. ?+?+?+?+⋯+?
Program Assignment07implicit noneinteger, parameter :: n = 1000 ! maximum iterationreal(kind=8), parameter :: EPSILON = 1.d-3real(kind=8):: x0,xinteger:: iterationx0=3.0d0call solve(f(x),fp(x),x0,n,x,iteration) contains real (kind=8) function f(x) ! this is f(x)implicit nonereal (kind=8), intent(in)::xf=x**2.0d0-1.0d0end function f real (kind=8) function fp(x) ! This is f'(x)implicit nonereal (kind=8), intent(in)::xfp=2.0d0*xend function fp end program Assignment07 modify this program in fortran byy adding a module (called Newton) which contains subroutinesolve. You should develop subroutine solve based on the aforementioned Newton's method. ▪ Function f(x) is x2-1 whose zero is known. Set the input argument EPSILON to 1.E-3 and inputargument n to 1000 when you call subroutine solve and run the program Modify the function to one that is known not to have zeros; e.g. (x2+1)
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…

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5. The growth of functions questions. A) True or False? • 3" is O (2ª") TRUTH FALSE • If f(n) = 1 + 3 + 2 + 4 + 3 * 5+ ..n • (n + 2) then f(n) is 0(n²) TRUTH FALSE