5.1.2.1. Types of Equations

Try these first

1. 1.

   Define an algebraic equation.

   Hint

   Think of simple math expressions.

2. 2.

   What is the Bisection Method?

   Hint

   Recall the interval where the function changes signs.

3. 3.

   What type of equation includes polynomial expressions?

   • Algebraic
   • Transcendental
   • Both

   Hint

   Think about basic algebra.

4. 4.

   The Newton-Raphson Method requires knowledge of what?

   • True
   • False

   Hint

   What do you need to draw a tangent line?

5. 5.

   Solve the transcendental equation sin(x) = 0.5 using the Newton-Raphson method starting with an initial guess of x = 0.5.

   Hint

   Remember to update using: `x_{n+1} = x_n - f(x_n) / f'(x_n)`.

6. 6.

   Create a practical example where you might encounter a transcendental equation in a real-world engineering scenario, and outline the necessary numerical method to solve it.

   Hint

   Identify the rearrangement of the equation you could use.