5.1.3.1. Bisection Method

Try these first

1. 1.

   What is the Bisection Method used for?

   Hint

   Think about equations that set equal to zero.

2. 2.

   Define a continuous function.

   Hint

   Consider the graph of the function.

3. 3.

   What is the primary function of the Bisection Method?

   • Find roots of continuous functions
   • Solve linear equations
   • Evaluate integrals

   Hint

   Remember, it helps find when the function crosses zero.

4. 4.

   True or False: The Bisection Method can be applied to functions that are not continuous.

   • True
   • False

   Hint

   Consider what discontinuities might imply about roots.

5. 5.

   You are tasked to find the root of f(x) = x^4 - 3x^3 + 2 within the interval [1, 2] using the Bisection Method. Show all calculations and steps to reach the root.

   Hint

   Pay attention to where the function transitions from positive to negative.

6. 6.

   Analyze the convergence rate of the Bisection Method by comparing it with a numerical result from the Newton-Raphson method for the equation f(x) = e^x - 1 within the interval [0, 1].

   Hint

   Think about how the methods approach roots and what information they use.