Table of Contents

## How is the bisection method used in Python?

The bisection method uses the intermediate value theorem iteratively to find roots. Let f (x) be a continuous function, and a and b be real scalar values such that a < b. Assume, without loss of generality, that f (a) > 0 and f (b) < 0. Then by the intermediate value theorem, there must be a root on the open interval (a, b).

## How is the bisection method used to find roots?

The bisection method uses the intermediate value theorem iteratively to find roots. Let f ( x) be a continuous function, and a and b be real scalar values such that a < b. Assume, without loss of generality, that f ( a) > 0 and f ( b) < 0. Then by the intermediate value theorem, there must be a root on the open interval ( a, b).

**How is the intermediate value theorem used in bisection?**

The Intermediate Value Theorem says that if f ( x) is a continuous function between a and b, and sign ( f ( a)) ≠ sign ( f ( b)), then there must be a c, such that a < c < b and f ( c) = 0. This is illustrated in the following figure. The bisection method uses the intermediate value theorem iteratively to find roots.

### How does the bisection method converge to a solution?

As you can see, the Bisection Method converges to a solution which depends on the tolerance and number of iteration the algorithm performs. There is a dependency between the tolerance and number of iterations. For a particular tolerance we can calculate how many iterations n we need to perform.

### Which is an example of a recursive function in Python?

Recursive Function in Python. Following is an example of a recursive function to find the factorial of an integer. Factorial of a number is the product of all the integers from 1 to that number. For example, the factorial of 6 (denoted as 6!) is 1*2*3*4*5*6 = 720.