Can any netizen answer what the dichotomy in high school math is?

The third chapter of the Mathematics Compulsory 1 of the A version of the People's Education.

For the function y=f(x) which is continuous on the interval [a,b] and f(a)·f(b)<0, the method of obtaining the zero approximation of the zero point by continuously dividing the interval where the zero point of the function f(x) is located in two, so that the two endpoints of the interval are gradually approaching the zero point, and then obtaining the zero approximation is called the dichotomous method.

Typical algorithms. Algorithm: This method is suitable when the amount of data is large. When using a dichotomous search, the data needs to be ordered. Let's mold shirt.

Basic idea: Assuming that the data is sorted in ascending order, for a given value key, the comparison starts at the middle position k of the open cavity of the sequence.

If the arr[k] value of the current location is equal to the key, the lookup is successful.

If the key is less than the current position value arr[k], the first half of the sequence is searched, arr[low,mid-1].

If the key is greater than the current position value arr[k], the code wheel will continue to find arr[mid+1,high] in the second half of the sequence.

Until found, time complexity: o(log(n)).

Classification: Resource Sharing.

Problem Description: An approximate solution to an equation using a dichotomous method.

Analysis: In general, for the function f(x), if there is a real number c, when x=c is f(c)=0, then x=c is called the zero point of the function f(x).

Solving the equation requires all zeros of f(x).

First find a, b, so that f(a), f(b) different signs, indicating that there must be zero points in the interval (a, b), and then find f[(a+b) 2], now assume f(a)<0, f(b)>0, a0, ditto.

By shrinking the interval where the zero point of f(x) is located by half each time, the two endpoints of the interval are gradually approaching the zero point of the function to obtain an approximate value of the zero point, which is called the dichotomy method.

Since the specific calculations of the calculation process are complex, but the way of each step is the same, it can be calculated by writing a program.

In fact, the dichotomy is not difficult, that is, according to the 0-point existence theorem to determine the interval of 0 points, and then constantly narrow the range of the intervals, so as to find the approximate value of 0 points or 0 points. But be sure to pay attention to the scope of application of the dichotomy. 1 consecutive 2 endpoint values with different signs (f(a)f(b)<0), otherwise the binary method cannot be used.

If there is anything you don't understand, you can add me to ask in detail.

Theorem: Knowing the function f(x) and the interval [a,b], if f(a)f(b)<0, then, there is a step for finding the zero point of the function with a dichotomy for the real number a:

1. Determine the interval between the zero point of the function (using the above theorem).

2. Find c=(a+b) 2

3. Judge whether f(c)=0 is true, if it is true, c is the zero point of the function, if not, proceed to the next step.

4. Judge whether f(a)f(c)<0 is true, if so, then the zero point of the function is on (a,c), so that b=c,; Otherwise, the zero point of the function is on (c,b), so that a=c.

5. Judgment|a-b|

f(2)=8-4-1=3>0

f(<0

The interval in which the root is located is ( ,2).

Choose d is happy to answer for you, I wish you good progress in your learning! The Learning Guide team will answer the questions for you.

d。The first thing to understand is what is a dichotomy, in layman's terms, is to take the middle number of two numbers (so you can exclude a and b), bring it into the equation, and see the change trend. Now bring x= into the equation and get <0.

The whole equation is monotonically increasing at x>1, so in order for the original equation to be equal to 0, this number must be (,2).

Let f(x)=x -2x-2

When x = 2, f(2) = 4-4-2 = -2

When x = 3, f(3) = 9-6-2 = 1

So there is a solution in (2, 3).

When x=, f(

There is a question to know x=

I'll show you how.

The dichotomy is to reduce the interval by half each time.

So divide (1,2) into (1,,2).

Then determine which interval it is.

Judgment method: Bring the two endpoints of the interval to the left side of the equation, if the signs are different, it is the solution interval.

So the result is (,2).