Exercises for Lecture 6

6.5. Exercises for Lecture 6#

6.5.1. Exercise 6.1#

Determine the zero of the function g(x) = cos(x) using the bisection method in the interval (0, 4).

Which checks have been omitted in the implementation of the algorithm described in the lesson text that could speed up the result?

6.5.2. Exercise 6.2#

Perform the previous exercise using a recursive function.

Which of the two implementations is faster?

6.5.3. Exercise 6.3#

Implement a function that calculates the factorial of a number using a recursive function.

6.5.4. Exercise 6.4#

Determine the minimum of the function g(x) = x² + 7.3x + 4 using the golden ratio search method in the interval (-10, 10).

6.5.5. Exercise 6.5#

Perform the previous exercise using a recursive function.

Which of the two implementations is faster?

6.5.6. Exercise 6.6#

Complete the two previous exercises by finding the maximum of a chosen function.

6.5.7. Exercise 6.7#

Modifying the previously developed programs, use matplotlib to plot the studied functions and the points found using the bisection and golden section search methods.