# Bisection Method Homework: a=-2, b=2, Is b-a=1?

• fonseh
In summary, the conversation discusses the meaning of the interval [-2,2] and how to show that b-a=1. There is a question about why b-a=-1-(-2), but this is incorrect as b and a have different roles in this context. The exercise suggests applying the bisection method on the interval [-2,-1] and for the second question, |b-a|=|-1-(-2)|=|1|=1.
fonseh

## Homework Statement

In the first photo , interval [-2 ,2 ] means a = -2 , b = 2 , am i right ?
So , how to show that b-a = 1 ?

## The Attempt at a Solution

IMO , b-a = 2+ 2 = 4

for part b , why b - a = -1-(-2) ?
Is there anything wrong with this question ?

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fonseh said:
interval [-2 ,2 ] means a = -2 , b = 2 , am i right ?
Not so: b and a play different roles.
Refer to example 2.3 for how to choose ##[a,b]##

##[-2,2]## is the interval for which the functions are considered.
The exercise suggests to apply the bisection method on another interval, namely ##[-2,-1]## because you don't need to consider the entire range. For the second question ##|b-a|=|-1-(-2)|=|1|=1##.

fonseh

## 1. What is the Bisection Method?

The Bisection Method is a numerical method used to find the root of a function. It involves repeatedly bisecting an interval and checking which sub-interval the root lies in until the root is found.

## 2. How does the Bisection Method work?

The Bisection Method works by taking an initial interval [a, b] and checking if the function changes sign at the midpoint of the interval. If it does, the root must lie in one of the sub-intervals, and the process is repeated until the root is found.

## 3. What are the conditions for using the Bisection Method?

The Bisection Method can only be used if the function is continuous on the given interval and changes sign at the endpoints of the interval. Additionally, the function must have a root within the interval [a, b].

## 4. How do the values of a and b affect the accuracy of the Bisection Method?

The values of a and b determine the initial interval and therefore affect the accuracy of the Bisection Method. A smaller interval will result in a more accurate approximation of the root, but it may also take more iterations to converge.

## 5. Is b-a=1 necessary for using the Bisection Method?

No, b-a=1 is not a necessary condition for using the Bisection Method. As long as the function is continuous on the interval [a, b] and changes sign at the endpoints, the method can be applied. However, choosing a smaller interval can result in a more accurate solution.

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