N 01: Intermediate Value Theorem & Bitsection Method

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Ex1.

Ex2.

 

 

 

 

 

Ex3.

1. Use the Bisection Method to find the root to six correct decimal places. (a) x3 = 9
(b) 3x3 + x2 = x + 5 (c) cos2 x + 6 = x

 

Ex4.

3. Consider the equations in Exercise 1. Apply two steps of the Bisection Method to find an
approximate root within 1/8 of the true root.

Ex5.

5. Consider the equation x4 = x3 + 10.
(a) Find an interval [a,b] of length one inside which the equation has a solution.
(b) Starting with [a,b], how many steps of the Bisection Method are required to calculate the
solution within 10−10? Answer with an integer.