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3. Problem 3: Find two roots of the equation cos(x)e-2sin(3 In (x²)) = 0, on the interval [4, 10]. Explain how many decimal places you believe you have correct, and how many steps of the bisection method it took. Also include timing results for your calculations.

3. Problem 3: Find two roots of the equation cos(x)e-2sin(3 In (x²)) = 0, on the interval [4, 10]. Explain how many decimal places you believe you have correct, and how many steps of the bisection method it took. Also include timing results for your calculations.

C++ for Engineers and Scientists
C++ for Engineers and Scientists
4th Edition
ISBN:9781133187844
Author:Bronson, Gary J.
Publisher:Bronson, Gary J.
Chapter14: Numerical Methods
Section14.3: Refinements To The Bisection Method
Problem 4E
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Please use python and show codes. The second picture is a different example we did
import math import time #Want a root of f(x) = cos(x) x^2/2 def f(x): return math.cos(x) tol=10**-15 a = 0.5 b = 1.5 Error = c = math.nan count = 0 (b-a)/2 tic time.time() if f(a) f(b) < 0: while (Error > tol) and (count < 1000): X c = (a+b)/2 if f(a) f(c) < 0: b = c elif f(b) f(c) < 0: a = c Error = (b-a)/2 count = count + 1 toc = time.time() runTime = toc - tic print () print (c) print (Error) print (f(c)) print (runTime) print (count) print()
Transcribed Image Text:import math import time #Want a root of f(x) = cos(x) x^2/2 def f(x): return math.cos(x) tol=10**-15 a = 0.5 b = 1.5 Error = c = math.nan count = 0 (b-a)/2 tic time.time() if f(a) f(b) < 0: while (Error > tol) and (count < 1000): X c = (a+b)/2 if f(a) f(c) < 0: b = c elif f(b) f(c) < 0: a = c Error = (b-a)/2 count = count + 1 toc = time.time() runTime = toc - tic print () print (c) print (Error) print (f(c)) print (runTime) print (count) print()
3. Problem 3: Find two roots of the equation cos(x)e-2sin (3 ln(x²)) = 0, on the interval [4, 10]. Explain how many decimal places you believe you have correct, and how many steps of the bisection method it took. Also include timing results for your calculations.
Transcribed Image Text:3. Problem 3: Find two roots of the equation cos(x)e-2sin (3 ln(x²)) = 0, on the interval [4, 10]. Explain how many decimal places you believe you have correct, and how many steps of the bisection method it took. Also include timing results for your calculations.
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