5.1.6. Applications

Try these first

1. 1.

   What is an algebraic equation? Give an example.

   Hint

   Think of polynomial expressions.

2. 2.

   What is a transcendental equation?

   Hint

   Look for sin, log, or e in your examples.

3. 3.

   What is the first step in applying the Bisection Method?

   • Choose any two points
   • Verify the function's continuity
   • Calculate the derivative

   Hint

   Focus on the requirements of the method.

4. 4.

   True or False: The Secant Method requires derivative calculations.

   • True
   • False

   Hint

   Think about the method's operational structure.

5. 5.

   Consider the function f(x) = x^2 - 3x + 2. Use the Bisection method to find the root(s) in the interval [0,3].

   Hint

   Make sure to keep track of the function values.

6. 6.

   Using the Newton-Raphson Method, find a root for g(x) = cos(x) - x, starting with an initial guess of x0 = 0.5.

   Hint

   Calculate each derivative carefully for accuracy.