Introduction to Algorithms
3rd Edition
ISBN: 9780262033848
Author: Thomas H. Cormen, Ronald L. Rivest, Charles E. Leiserson, Clifford Stein
Publisher: MIT Press
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Chapter 3.2, Problem 4E
Program Plan Intro
To check whether the functions
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- code required for python: 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. my code below , however as…arrow_forwardCompute and plot the derivative of the function f(x) = x³ • Apply the above methodology to compute and plot the derivative of the function f(x) = x³, for x = [-n, n], for n = 5 and 8 In [39]: import matplotlib.pyplot as plt n = 5 r = list (range(-n, n+1)) cubes = [] ## generate the squares using a for Loop for value in r: s = value**3 cubes.append(s) slopes = [] first = b = ## generate plot points from existing lists plt.plot(r, cubes, label = 'function line') plt.plot(r, cubes, 'ro', label = 'function points') plt.plot(r, slopes, label = 'slope line') plt.plot(r, slopes, 'go', label = 'slope points') plt.plot(r, trueslope, label = 'true slope') # generate axes Lables plt.ylabel('cubes value') plt.xlabel('integer input') plt.title('cubes plot') plt.legend() # display plot plt.show()arrow_forwardL₁ = {abman: n ≥ 0, m>0} Use the rule of contradiction, prove that following language is regular or not.arrow_forward
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