5.1.1. Introduction

Try these first

1. 1.

   What are algebraic equations? Provide an example.

   Hint

   Remember the operations involved: addition, subtraction, multiplication, etc.

2. 2.

   What is an example of a transcendental equation?

   Hint

   Think about functions that are not polynomials.

3. 3.

   What type of equations often require numerical methods for solutions?

   • Algebraic Equations
   • Linear Equations
   • Transcendental Equations

   Hint

   Consider the nature of transcendental functions.

4. 4.

   True or False: The Bisection Method requires the derivative of the function.

   • True
   • False

   Hint

   Recall the conditions for the Bisection Method.

5. 5.

   Given the equation 𝑥² - 5 = 0, apply the Bisection Method to find a root with an interval of [2, 3] and a tolerance of 0.01. Demonstrate your calculations.

   Hint

   Start calculating f(2) and f(3) and check the value of the function.

6. 6.

   For the equation 𝑒ˣ = 3𝑥, apply the Newton-Raphson method starting with an initial guess of 1. Find the root up to three decimal places.

   Hint

   Make sure to differentiate the function to get your f'(x).