For this question, you will be required to use the binary search to find the root of some function f(x)f(x) on the domain x∈[a,b]x∈[a,b] by continuously bisecting the domain. In our case, the root of the function can be defined as the x-values where the function will return 0, i.e. f(x)=0f(x)=0For example, for the function: f(x)=sin2(x)x2−2f(x)=sin2(x)x2−2 on the domain [0,2][0,2], the root can be found at x≈1.43x≈1.43ConstraintsStopping criteria: ∣∣f(root)∣∣<0.0001|f(root)|<0.0001 or you reach a maximum of 1000 iterations.Round your answer to two decimal places.Function specificationsArgument(s):f (function) →→ mathematical expression in the form of a lambda function.domain (tuple) →→ the domain of the function given a set of two integers.MAX (int) →→ the maximum number of iterations that will be performed by the function.Return:root (float) →→ return the root (rounded to two decimals) of the given function. START FUNCTIONdef binary_search(f,domain, MAX = 1000): f = lambda x:(np.sin(x)**2)*(x**2)-2domain = (0,2)x=binary_search(f,domain)x testbinary_search(lambda x:(np.sin(x)**2)*(x**2)-2,(0,2))==1.43

import numpy as npdef binary_search(f,domain, MAX = 1000): start ,end = domain # get the start and…

Answered: For this question, you will be required…

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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For this question, you will be required to use the binary search to find the root of some function f(x)f(x) on the domain x∈[a,b]x∈[a,b] by continuously bisecting the domain. In our case, the root of the function can be defined as the x-values where the function will return 0, i.e. f(x)=0f(x)=0

For example, for the function: f(x)=sin2(x)x2−2f(x)=sin2(x)x2−2 on the domain [0,2][0,2], the root can be found at x≈1.43x≈1.43

Constraints

Stopping criteria: ∣∣f(root)∣∣<0.0001|f(root)|<0.0001 or you reach a maximum of 1000 iterations.
Round your answer to two decimal places.

Function specifications

Argument(s):

f (function) →→ mathematical expression in the form of a lambda function.
domain (tuple) →→ the domain of the function given a set of two integers.
MAX (int) →→ the maximum number of iterations that will be performed by the function.

Return:

root (float) →→ return the root (rounded to two decimals) of the given function.

START FUNCTION

def binary_search(f,domain, MAX = 1000):

f = lambda x:(np.sin(x)**2)*(x**2)-2

domain = (0,2)

x=binary_search(f,domain)

test

binary_search(lambda x:(np.sin(x)**2)*(x**2)-2,(0,2))==1.43

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