Answer:
The regular falsi method, also known as the false position method, is a numerical method for finding the root of an equation. It is a variant of the bisection method and is used when the function is not continuous or when the bisection method is too slow.
To find the real root of the equation x tan x + 1 = 0 using the regular falsi method, you will need to:
Choose two initial guesses for the root, x0 and x1.
Evaluate the function at each of the guesses and note their signs.
Use the following formula to calculate the next guess for the root, x2:
x2 = x1 - f(x1) * (x1 - x0) / (f(x1) - f(x0))
Evaluate the function at the new guess and note its sign.
If the sign of the function at x2 is the same as the sign at x0, update x0 to x2 and repeat the process from step 3.
If the sign of the function at x2 is the same as the sign at x1, update x1 to x2 and repeat the process from step 3.
Repeat the process until x2 is close enough to the root or until a maximum number of iterations is reached.
It's important to note that this method is not as efficient as other method like newton-raphson, bisection and secant method.