Problem 3: Find two roots of the equation cos(r)e-2 sin(3 ln(2²)) = 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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Please use python and show the codes. The second picture is an example
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.
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()
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