5.1.2.1.2. Transcendental Equations

Try these first

1. 1.

   What is the main difference between algebraic and transcendental equations?

   Hint

   Think about the types of functions involved.

2. 2.

   What is required for the Bisection Method to start?

   Hint

   Consider under what conditions the root exists.

3. 3.

   What type of equations involve non-algebraic functions?

   • Algebraic Equations
   • Transcendental Equations
   • Linear Equations

   Hint

   Focus on the equation type that is not polynomial.

4. 4.

   True or False: The Bisection Method can guarantee finding a root as long as the function is continuous in the chosen interval.

   • True
   • False

   Hint

   Consider the properties of continuous functions.

5. 5.

   For the equation x^2 - 3 = 0, demonstrate using the Bisection method starting from [1, 2] to reach a root to two decimal places.

   Hint

   Narrow down in each step based on function signs.

6. 6.

   Use the Newton-Raphson method for f(x) = e^x - 2 while starting with an initial guess of x=0. How many iterations will it take to achieve an accuracy of 10^-5?

   Hint

   Calculate function values and update using the tangent each step.