import javax.swing.JOptionPane;

/**

* Driver to estimate the limit of one of several functions

* as x goes to a specified value from the left

* @author ralexander

*

*/

public class EstimateLimit {

private static Function fn;

public static void main(String[] args) {

//declare local variables

int fnVersion = 0;

double x = 0.0;

String input;

boolean again = false;

//do loop that repeats if user wants to estimate another limit

do {

//displays the options and prompts the user to choose one

//this should not be hardwired, but call the getDescription(i) methods of the Function class

input = JOptionPane.showInputDialog(null,"This program estimates the limit of a function (from the left) "+

"The functions to choose from are: "+

" 1. "+Function.getDescription(1)+" "+

" 2. "+Function.getDescription(2)+" "+

" 3. "+Function.getDescription(3)+" "+

" 4. "+Function.getDescription(4)+" "+

" 5. "+Function.getDescription(5)+" "+

"For which function do you want to estimate the limit? (1 - 5)");

//parses the string into an integer.

//Does not catch a non-integer entry - will cause an unhandled exception

fnVersion = Integer.parseInt(input);

//while loop to ensure choices are between 1 and 5

while(fnVersion5) {

input = JOptionPane.showInputDialog(null,"Input must be 1, 2, 3, 4, or 5. Try again ");

fnVersion = Integer.parseInt(input);

}

//create the chosen function instance

fn = new Function(fnVersion);

//user enters the value that x goes to

input = JOptionPane.showInputDialog(null,"As x goes to what value (from the left)?");

//parses the string result into a double

x = Double.parseDouble(input);

//call the method to estimate the limit

estimateLimit(x);

//prompt the user to ask if he/she wants to estimate another limit

String againString = JOptionPane.showInputDialog(null,"Do you want to try again? (y or n)");

//if the user entered y, set the boolean again to true

if (againString.equals("y")) {

again=true;

}

//if the user entered anything except y, set the boolean again to false

else {

again=false;

System.out.println("Goodbye");

}

}

while(again);

}

/**

* the method estimateLimit computes the approximate value of the chosen function ten times, coming closer

* and closer to f(x) as x gets closer and closer to the desired value from the left

* @param functionChoice one of five integers that represents the five functions

* @param x the user's input to the limit of the function

*/

private static void estimateLimit(double x) {

//false if the function diverges, true if the limit exists

boolean limitExists = true;

//whether or not the user wants to repeat the process

boolean again=true;

//to test if the function is diverging, we need to know the previous value of the function

double previousResult=0;

//the current value of the function

double result=0;;

System.out.println("Estimating the limit of "+fn+" as x goes to "+x+" from the left");

//System.out.println("Estimating the limit of f"+fn.getFunctionChoice()+"(x) as x goes to "+x+" from the left");

//back x off by 1.0 to approach limit from the left

x--;

//a for loop that will loop ten times, or until it is determined that the function is diverging

for (int i=1; (i

//for each iteration of the for loop, calculate the value of the function with a closer and closer value of the input

result = calcFunction(x+=(9/Math.pow(10,i)));

//an if statement that tests if the previous result is more than 1.0 away from the current result

//the if statement ensures that at least five iterations are done before testing for divergence

if ((i > 5)&&Math.abs(previousResult-result)>1.0) {

JOptionPane.showMessageDialog(null, "Diverging: estimate that limit of "+fn+" as x->"+(Math.round(x*100))/100.0+" does not exist");

limitExists = false;

}

else {

System.out.println("for x = "+x+", "+fn+" = "+result);

previousResult = result;

}

}

//an if statement that shows the estimated limit if the limit exists, rounded to two decimal places

if (limitExists) {

JOptionPane.showMessageDialog(null, "Estimate that the limit of "+fn+" as x->"+(Math.round(x*100))/100.0+" is "+(Math.round(result*100))/100.0);

}

}

/**

* calcFunction calls the appropriate function calculation

* @param functionChoice the function the user has selected

* @param x the current input to the function, getting closer and closer to the desired

* value with each call to this function

* @return a double which is the value of the function at x

*/

private static double calcFunction(double x) {

return fn.computeFunctionValue(x);

}

}

Paragraph Introduction In this lab we will create several functions with methods for each, and allow the user to the limit from the left of each function. You will create a class called "Function" that will be run by a "driver" class called "Estimatel imit", which is provided Your class will have the following fields: CHOICE - this is an integer constant that references the function the user selects . description this is a string that describes the chosen function. The class will bave the following methods: getFunctionChoice-this is an accessor the returns the index of the chosen function setDescription-this sets the description field with a string that describes the chosen function. getDescription - this is an accessor that takes an integer indexing one of the functions and returns the string describing the function. This method is used before the user has chosen a function, to list each of the descriptions * toString-t this is a method that is already defined for any object in lava. We are "overriding" it to have it return the string which describes the chosen function computeFunctionValue- this takes a value for x and computes the value of the function fx) We will also need a constructor method that willbe used to create an instance of a Function Function- this takes the index of the chosen function, sets the constant that indexes t on and sets the description. It returns the instance (i.e, the object) that will be used These ideas can be brought together to form a UML (Unified Modeling Language) diagram for this class as shown below. Function Class name + public private FUNCTION_CHOICE: double Fields description:String Methods + Function (fnChoiceint) getFunctionChoice)int setDescription) +getDescription (fnChoice:int)-String +toString):String + computeFunctionValue(xcdouble) doyble Return type Task #1 Creating a New Class 1. In a new file, create a class definition called Function. 2. Put a program header (comments/documentation) at the top of the file in Javadoc format: The purpose of this class is Your name and today's date 3. Declare the fields listed in the UML diagram. 4. Write a comment for each field indicating what it represents. 5. Save this file as Function.java. 6. Compile and debug. Do not run