Optimization: make the input as big or as small as possible in Python using Newton and Bisection methods. The picture below is an example from another problem we did (newton). Please show your codes. 2.ƒ(x)= 10 ln1x² +1e import mathimport time#Want a root of f(x) = cos(x) = x^2/2def f(x):return math.cos(x) - Xtol=10**-15a = 0.5b = 1.5Error (b-a)/2c = math.nancount = 0tic time.time()if f(a) f(b) < 0:while (Error > tol) and (count < 1000):c = (a+b)/2if f(a) f(c) < 0:b = celif f(b) f(c) < 0:a = cErrorcount(b-a)/2count + 1toc time.time()runTime toc - ticprint ()print (c)print (Error)print (f(c))print (runTime)print (count)print ()

The given function is:- fx=10ln1x2+1×e-x2+x Python Introduction:- Python is a dynamic, interpreted…

Answered: 10 In (²+1) • e 2.ƒ(x)= 10ln ·(1²+1)

Database System Concepts

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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

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Optimization: make the input as big or as small as possible in Python using Newton and Bisection methods. The picture below is an example from another problem we did (newton). Please show your codes.

import math
import time
#Want a root of f(x) = cos(x) = x^2/2
def f(x):
return math.cos(x) - X
tol=10**-15
a = 0.5
b = 1.5
Error (b-a)/2
c = math.nan
count = 0
tic time.time()
if f(a) f(b) < 0:
while (Error > tol) and (count < 1000):
c = (a+b)/2
if f(a) f(c) < 0:
b = c
elif f(b) f(c) < 0:
a = c
Error
count
(b-a)/2
count + 1
toc time.time()
runTime toc - tic
print ()
print (c)
print (Error)
print (f(c))
print (runTime)
print (count)
print ()

Expert Solution

Step 1

The given function is:-

$f (x) = 10 \ln (\frac{1}{x^{2} + 1}) \times e^{- (x^{2} + x)}$

Python Introduction:-

Python is a dynamic, interpreted language that uses bytecode compilation. The source code lacks type definitions for variables, parameters, functions, or methods. As a result, the source code's compile-time type checking is lost, but the code is short and flexible. Python keeps track of the types of each value at runtime and highlights any code that does not make sense.

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