Using bisection method to find p3 for f(x) = sqrt(x) - cos(x), I got the right answer on paper p3 = .625

I am having a trouble converting the problem and solving it using Jupyter notebook. Any tips?

Jupyter Notebook code

CodePudding user response：

0.625 is the third guess in the approximation process so the for loop should be completed before the fourth iteration and the code should be as follows.

import math

##problem statement
#finding a root of f(x) = sqrt(x)-cos(x) between the interval [0,1]
#f(0) = -1 f(1) = 0.45969..  so there is at least one root between the interval [0,1]

a = 0
b = 1
maxIt = 100
negative_result = math.sqrt(a) - math.cos(a)
positive_result = math.sqrt(b) - math.cos(b)

for i in range(maxIt):
    if i == 3:
        print("answer is: ", guess)
        break
    guess = (a b)/2
    guess_result = math.sqrt(guess) - math.cos(guess)
    if guess_result*negative_result >= 0:
       a = guess
    else: 
        b = guess

And the output is

0.625