In this video, we tackle the intriguing equation (1/2)^x=x. oin us as we explore the analytical approach to understanding this equation and discover why it leads us to a numerical solution. We will use Python to find the approximate value of x approximately equal to 0.6412. This video is perfect for math enthusiasts, students, and educators looking to deepen their understanding of solving complex equations involving exponential and linear functions.
#maths #mathematics #algebra
Python code:# Bisection Method in Python
def f(t):
return t**t - 2
def bisection_method(f, a, b, tol=1e-5):
if f(a) * f(b) great or equal 0:
print("Bisection method fails.")
return None
a_n = a
b_n = b
while (b_n - a_n) / 2 greater tol:
midpoint = (a_n + b_n) / 2
if f(midpoint) == 0:
return midpoint # The midpoint is the root
elif f(a_n) * f(midpoint) less than 0:
b_n = midpoint
else:
a_n = midpoint
return (a_n + b_n) / 2
Define the interval
a = 0.5
b = 2
Find the root
root = bisection_method(f, a, b)
print(root)
Негізгі бет Solve (1/2)^x=x Using Analytical and Numerical Method
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