Math Problem Statement
Write down step by step maths solution to Compute the real root of f(x) = x − 2sin(x) = 0 correct upto 6 decimal places using Regula Falsi Method where output will be:1.8954942. solve x2 = x0 - [(x1 - x0)/(f(x1) - f(x0))] × f(x0).Where f(1) = 1 - 2sin(1) ≈ 1 - 1.6829 ≈ -0.6829 f(2) = 2 - 2sin(2) ≈ 2 - 1.8186 ≈ 0.1814
Solution
We aim to solve f(x) = x − 2sin(x) = 0 using the Regula Falsi Method (False Position Method). Here's the step-by-step procedure:
Step 1: Define the Function and Initial Guess
The function is:
From the problem:
- Initial guesses are and .
- Evaluate and :
- ,
- .
and have opposite signs, confirming a root exists in the interval .
Step
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Math Problem Analysis
Mathematical Concepts
Numerical Methods
Root-Finding Algorithms
Regula Falsi Method
Formulas
x2 = x0 - [(x1 - x0) / (f(x1) - f(x0))] × f(x0)
f(x) = x − 2sin(x)
Theorems
Intermediate Value Theorem
Suitable Grade Level
Undergraduate (Numerical Methods or Calculus Course)