The square root of any number N>0 can be opproximated by repeated calculation using the formula N - squared_value NG - 0.5 (FG + N/FG) where NG stands for next guess and FG stands for first guess. The value of NG and FG are compared. If the two values are comparably close, then NG is the final answer. If the two values are off, NG becomes FG and the formula is used again to compute FG. After so many iterations, NG and FG will merge. a. Write a function that calculates the square root of a number using this method. The initial guess will be the starting value of FG (FG - 1). The function will compute a value for NG using the formula given and returns that value. (Change the name of the functions to something more meaningful) double fun_1 (double FG, double N); b. Write a function that prompts the user for any number N > 0, and returns that value back. The prototype is like follows: double fun_2 ( void );
The square root of any number N>0 can be opproximated by repeated calculation using the formula N - squared_value NG - 0.5 (FG + N/FG) where NG stands for next guess and FG stands for first guess. The value of NG and FG are compared. If the two values are comparably close, then NG is the final answer. If the two values are off, NG becomes FG and the formula is used again to compute FG. After so many iterations, NG and FG will merge. a. Write a function that calculates the square root of a number using this method. The initial guess will be the starting value of FG (FG - 1). The function will compute a value for NG using the formula given and returns that value. (Change the name of the functions to something more meaningful) double fun_1 (double FG, double N); b. Write a function that prompts the user for any number N > 0, and returns that value back. The prototype is like follows: double fun_2 ( void );
Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Chapter1: Introduction
Section: Chapter Questions
Problem 1PE
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![**Approximating the Square Root of a Number**
The square root of any number \( N>0 \) can be approximated through repeated calculations using the following formula:
\[
\text{N} = \text{squared\_value}
\]
\[
\text{NG} = 0.5(\text{FG} + \text{N/FG})
\]
Here, NG stands for the next guess and FG stands for the first guess. The values of NG and FG are compared. If the two values are comparably close, then NG is the final answer. If the two values are off, NG becomes FG and the formula is used again to compute FG. After several iterations, NG and FG will converge.
### Tasks
a. **Function to Calculate the Square Root:**
Write a function that calculates the square root of a number using this method. The initial guess will be the starting value of FG (\(\text{FG} = 1\)). The function will compute a value for NG using the formula given and return that value. (Change the name of the function to something more meaningful.)
```c
double fun_1 (double FG, double N);
```
b. **User Input Function:**
Write a function that prompts the user for any number \( N > 0 \), and returns that value back. The prototype is as follows:
```c
double fun_2 ( void );
```
c. **Main Function Logic:**
Now inside the main function, check the difference between NG and FG to see whether these two guesses are almost identical. If they are, NG is accepted as the square root; otherwise, the first guess (FG) becomes the next guess (NG) and the process is repeated (another value is computed for NG, the difference is checked, and so on). The loop should be repeated until the difference \((|\text{NG - FG}|)\) is less than 5e-3.
d. **Test Cases:**
Test your square root function for the numbers:
- 6
- 120.5
- 88
- 36.01
- 10000
- 0.25
For each number, display the estimated square root value, the number of iterations, and the error value (difference of two iterations).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F04c52921-cfa4-41e1-9a17-e97aadee2312%2F922a7310-27e1-4e2d-be79-8ca78e7f3eb7%2F2oj2qaq_processed.png&w=3840&q=75)
Transcribed Image Text:**Approximating the Square Root of a Number**
The square root of any number \( N>0 \) can be approximated through repeated calculations using the following formula:
\[
\text{N} = \text{squared\_value}
\]
\[
\text{NG} = 0.5(\text{FG} + \text{N/FG})
\]
Here, NG stands for the next guess and FG stands for the first guess. The values of NG and FG are compared. If the two values are comparably close, then NG is the final answer. If the two values are off, NG becomes FG and the formula is used again to compute FG. After several iterations, NG and FG will converge.
### Tasks
a. **Function to Calculate the Square Root:**
Write a function that calculates the square root of a number using this method. The initial guess will be the starting value of FG (\(\text{FG} = 1\)). The function will compute a value for NG using the formula given and return that value. (Change the name of the function to something more meaningful.)
```c
double fun_1 (double FG, double N);
```
b. **User Input Function:**
Write a function that prompts the user for any number \( N > 0 \), and returns that value back. The prototype is as follows:
```c
double fun_2 ( void );
```
c. **Main Function Logic:**
Now inside the main function, check the difference between NG and FG to see whether these two guesses are almost identical. If they are, NG is accepted as the square root; otherwise, the first guess (FG) becomes the next guess (NG) and the process is repeated (another value is computed for NG, the difference is checked, and so on). The loop should be repeated until the difference \((|\text{NG - FG}|)\) is less than 5e-3.
d. **Test Cases:**
Test your square root function for the numbers:
- 6
- 120.5
- 88
- 36.01
- 10000
- 0.25
For each number, display the estimated square root value, the number of iterations, and the error value (difference of two iterations).
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