Question

equation
y using regula falsi method, compute real root the
2x - log x = 7 correct to three decimal places. ​

Answer 1

Answer:

= 0 then c is the root. Selecting c by the above expression is called Regula-Falsi method or False position method. The false position method is again bound to converge because it brackets the root in the whole of its convergence process. Find a root of 3x + sin(x) - exp(x) = 0.

...

REGULA-FALSI METHOD.

c = b - f(b) * (b-a)

f(b) - f(a)

Step-by-step explanation:

Neglecting the negative sign, we get the rate of convergence for the Secant method (1) is P = 1.618. The Regula-Falsi method is also called as Regula-Falsi Method. This is oldest method for computing the real roots of an algebraic equation

The Regula–Falsi Method is a numerical method for estimating the roots of a polynomial f(x). A value x replaces the midpoint in the Bisection Method and serves as the new approximation of a root of f(x). The objective is to make convergence faster. Assume that f(x) is continuous

Answer 2

Given:

2x - log x = 7.

To Find:

The real root of the given equation.

Solution:

Let f(x) = 2x - log x - 7.

Taking x(0) = 3.5 and x(1) = 4 in the method of falsi position. We get,

$x(2) = x(0) - \frac{(x(1) - x(0))}{fx(1) - fx(0)} fx(0)$

Since, f(3.7888) = 0.0009 and f(u) = 0.3979.

Therefore, the root lies between 3.7888 and 4.

Taking x(0) = 3.7888 and x(1) = 4,

we will obtain,

$x(3) = 3.7888 - \frac{0.2112}{0.3988} ( - 0.009) = 3.789.$

Hence, the real root of the given equation upto three decimal places is 3.789.