Question

Let f(x)=2x^2-3, two initial guesses are x_1=0 and x_2=1.Find x_3 (numerical approximation with 2 iterations) using Secant method.

Answer 1

The Secant method is an iterative method used to approximate the roots of a function. Given two initial guesses, x₁ = 0 and x₂ = 1, so, x₃ is 2.

The Secant method is an iterative method used to approximate the roots of a function.

In this case, we are trying to find the value of x that makes the function f(x) = 2x² - 3 equal to zero.

We are given two initial guesses, x₁ = 0 and x₂ = 1.

To find x₃, we will use the formula for the Secant method: x₃ = x₂ - f(x₂) * (x₂ - x₁) / (f(x₂) - f(x₁)).

Substituting the values into the formula, we get x₃ = 1 - (2(1)² - 3) * (1 - 0) / ((2(1)² - 3) - (2(0)² - 3)) =

x₃ = 1 - (-1) / (-1)

x₃ = 2.