A calculator simplifies the bisection method.
Declaration of halving method
Often in mathematics zeros of a function are calculated. As long as a zero at the same time is not a high or low spot, zeros are characterized in that the y-values on the one hand are larger and less on the other side as zero. This is the basis for the Declaration of halving process. So is the procedure:
- In the bisection method, two x-values are wanted, with an associated y value is positive and one is negative.
- If these values are found, the average of the two x-values is used in the function.
- If the result is positive, the x-value, which includes the negative y-value is used. Otherwise, the other x-value is used in the following.
- Now again the mean value of the mean value of the point 2 and the to be used in x-value is formed and also used in the function.
- This procedure is repeatedly carried out successively until the zero point is found.
Since the best explanation is always an example, followed by a calculation example of the halving method.
Example for implementation of the method halving
- As an example, the function f (x) = -2x + 4.5 is given. Put x = 0 and you will get the corresponding y-value 4.5.
- Due to the negative slope and the positive y-intercept of the line you can see that you can get a negative y-value for a positive x value.
- So put an for x the number. 3 This will give you the corresponding y-value -1.2. Thus, the actual zero between these x-values must occur.
- The mean value between 0 and 3 is 1.5. Set this value so in the function. This will give you the corresponding y-value of 1.8.
- The zero point should be between the points (1.5 / 1.8) and (3 / 1.2) are. thus forming the mean value between 1.5 and 3. It is situated at 2.25.
- Put 2.25 in the function and you will receive 0 for the y value. Thus your zero is (2.25 / 0)
Other possible applications of the method
Of course, you could also calculate on a conventional manner, in the example the zero point. But especially with functions of higher degree, whose zeros can only be determined by polynomial division, the bisection method is a good help and complement. With this technique, but you can also roots, logarithms u. Ä. approach. So you do not know even how to resolve a function or mathematical expression for an unknown, just try to determine this number by the bisection method.