/*QUESTION 2:*/
/*Program: Finding real roots of nonlinear
   equation using Newton Method*/ 
#include<stdio.h>
#include<math.h>
#include<stdlib.h>

/* Defining equation to be solved.*/
#define f(x) exp(-2*x)-(x*exp(-2*x))-(3*exp(-x))+2
/* Defining derivative of g(x)*/
#define g(x) -2*exp(-2*x)+(2*x*exp(-2*x))-exp(-2*x)+(3*exp(-x))

void main()
{
	 float x0, x1, f0, f1, g0, e;
	 int step = 1, N;
     /* Inputs */
	 printf("\nEnter initial guess:\n");
	 scanf("%f",&x0);
	 printf("Enter tolerable error:\n");
	 scanf("%f",&e);
	 printf("Enter maximum iteration:\n");
	 scanf("%d",&N);
	 /* Implementing Newton Method */
	 printf("\nStep\t\tx0\t\tf(x0)\t\tx1\t\tf(x1)\n");
	 do
	 {
		  g0=g(x0);
		  f0=f(x0);
		  if(g0==0.0)
		  {
			   printf("Mathematical Error.");
			   exit(0);
		  }

		
		  x1 = x0 - (f0/g0);
		  printf("%d\t\t%f\t%f\t%f\t%f\n",step,x0,f0,x1,f1);
		  x0 = x1;
		  
		  step = step+1;
		
		  if(step > N)
		  {
			   printf("Not Convergent.");
			   exit(0);
		  }
		  
		  f1 = f(x1);
		  
	 }while(fabs(f1)>e);
	
	 printf("\nRoot is: %f", x1);
}
by

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About C

C language is one of the most popular general-purpose programming language developed by Dennis Ritchie at Bell laboratories for UNIX operating system. The initial release of C Language was in the year 1972. Most of the desktop operating systems are written in C Language.

Key features:

  • Structured Programming
  • Popular system programming language
  • UNIX, MySQL and Oracle are completely written in C.
  • Supports variety of platforms
  • Efficient and also handle low-level activities.
  • As fast as assembly language and hence used as system development language.

Syntax help

Loops

1. If-Else:

When ever you want to perform a set of operations based on a condition if-else is used.

if(conditional-expression) {
   // code
} else {
   // code
}

You can also use if-else for nested Ifs and if-else-if ladder when multiple conditions are to be performed on a single variable.

2. Switch:

Switch is an alternative to if-else-if ladder.

switch(conditional-expression) {    
case value1:    
 // code    
 break;  // optional  
case value2:    
 // code    
 break;  // optional  
...    
    
default:     
 // code to be executed when all the above cases are not matched;    
}

3. For:

For loop is used to iterate a set of statements based on a condition.

for(Initialization; Condition; Increment/decrement){  
  // code  
}

4. While:

While is also used to iterate a set of statements based on a condition. Usually while is preferred when number of iterations are not known in advance.

while(condition) {  
 // code 
}

5. Do-While:

Do-while is also used to iterate a set of statements based on a condition. It is mostly used when you need to execute the statements atleast once.

do {
  // code 
} while (condition);

Arrays

Array is a collection of similar data which is stored in continuous memory addresses. Array values can be fetched using index. Index starts from 0 to size-1.

Syntax

One dimentional Array:

data-type array-name[size];

Two dimensional array:

data-type array-name[size][size];

Functions

Function is a sub-routine which contains set of statements. Usually functions are written when multiple calls are required to same set of statements which increases re-usuability and modularity.

Two types of functions are present in C

  1. Library Functions:

Library functions are the in-built functions which are declared in header files like printf(),scanf(),puts(),gets() etc.,

  1. User defined functions:

User defined functions are the ones which are written by the programmer based on the requirement.

How to declare a Function

return_type function_name(parameters);

How to call a Function

function_name (parameters)

How to define a Function

return_type function_name(parameters) {  
  //code
}