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...

 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 or you="" reach="" a="" maximum="" of="" 1000="">


• 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)

x

test

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