Math Problem Statement

solve this with bisection for x0=0.1, 0.7 and 0.9 x.e^(x^2)-1=0 with a tolerance of 10^-4 with the iteration table

Solution

Here is the bisection method solution for the equation f(x)=xex2−1=0f(x) = x e^{x^2} - 1 = 0 using a tolerance of 10−410^{-4}, and the initial guesses x0=0.1x_0 = 0.1, x0=0.7x_0 = 0.7, and x0=0.9x_0 = 0.9.

Iteration Table Format:

For each iteration, we will display:

  • aa: Lower bound of the

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Math Problem Analysis

Mathematical Concepts

Numerical Methods
Bisection Method
Exponential Functions

Formulas

f(x) = x * e^{x^2} - 1
Bisection method formula: x_{n+1} = (a_n + b_n) / 2

Theorems

Intermediate Value Theorem (used in the bisection method)

Suitable Grade Level

College Level (Numerical Methods)

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