Getting an incorrect output for e^x function I made for class, and getting the wrong number of terms?

Question

So for my Intro to computer programming class we have to write 3 separate functions, one to calculate factorials, one to calculate powers (x^n), and one to calculate the number of terms of the taylor series with the given error approximation. Everytime I run my program, it prints that Nterms=1, instead of like 100, 300, 1000, etc. It's probably a simple error in my loop, but I can't locate it. Any help is appreciated! #include<stdio.h> #include<math.h> double power(float A, int B) {   double sum=1.00;   int nterms=1;     while ( nterms <= B && B > 0)   {    sum = A*sum;    nterms++;   }   return sum; } double factorial(int b) {   double fact=1.00;    while (b >= 2)   {    fact = b*(b-1)*fact;    b = b-2;   }     return fact;  } int Terms(float X, float a) {   int N=1,l;   double L,R;      while (L < a && a <= R)   { l=N+1;    L= (power(X,l)/(factorial(l)));    R= (power(X,N)/(factorial(N)));    N++;  }     return N; } int main() {     float x, delta; double sum=0.00, term=0.00;   int n, Nterms;     printf("Please enter a decimal number. x=");   scanf("%f",&x);   printf("Please enter an another number. delta=");   scanf("%f",&delta);     Nterms=Terms(x,delta);   printf("Nterms=%d\\n",Nterms);     for(n=0;n<Nterms;n++)   {    if( n==0 || n==1 )    {     sum = 1 + x;    }    else    {     sum = sum + term;     term = (power(x,n))/(factorial(n));    }    }    printf("The approximation for e^(%f)=%.4f",x,sum);     return 0; }

Answer 1

Your function terms apparently is calculating the minimum number of terms in the Taylor series needed to calculate exp(x) to an accuracy at least as good as the given delta.

e.g., for x = 1 (to calculate exp(1)), with a delta of 0.1, terms(1, 0.1) should return 5,

so exp(1) is approximately equal to 2.6667.

e.g., for x = 1, with a delta of 0.01, terms(1, 0.01) should return 6,

so exp(1) is approximately equal to 2.7083.

e.g., for x = 1, with a delta of 0.001, terms(1, 0.001) should return 8,

so exp(1) is approximately equal to 2.7181.

I did not have a working version of your terms(float X, float delta) function, because it had two uninitialized variables in it (L and R).

The following modification to your terms function seems to calculate the correct number of terms to calculate exp(x) correctly. To do this, the L variable was eliminated, the R variable was initialized, the while loop changed to only compare delta to the value of R, and the value of the l (lowercase L) was eliminated.

The printf statement was added to debug the number of terms Terms() was returning.

int terms(float X, float delta) {

int N = 1;

  double R = 100000;

  while (delta <= R) {

   R = (power(X, N) / (factorial(N)));

   N++;

  }

// printf("for %f, terms needed are: %d\n", delta, N);

  return N;

}

//----------------------------------------------------------------------------------------------------

// Complete code example:

//----------------------------------------------------------------------------------------------------

#include <stdio.h>

#include <math.h>

double power(float A, int B) {

double sum = 1.00;

  int nterms = 1;

  while ( nterms <= B && B > 0) {

   sum = A * sum;

   nterms++;

  }

  return sum;

}

double factorial(int b) {

double fact = 1.00;

  while (b >= 2) {

   fact = b * (b-1) * fact;

   b -= 2;

  }

  return fact;

}

int terms(float X, float delta) {

int N = 1;

  double R = 100000;

  while (delta <= R) {

   R = (power(X, N) / (factorial(N)));

   N++;

  }

  printf("for %f, terms needed are: %d\n", delta, N);

  return N;

}

int main() {

float x, delta;

  double sum = 0.00, term = 0.00;

  int n, Nterms;

  

printf("Please enter a decimal number. x=");

  scanf("%f", &x);

  printf("Please enter an another number. delta=");

  scanf("%f", &delta);  

Nterms = terms(x, delta);

for (n = 0; n < Nterms; n++) {

   if (n == 0 || n == 1 ) {

    sum = 1 + x;

   } else {

    sum += term;

    term = (power(x,n)) / (factorial(n));

   }

  }

  printf("The approximation for e^(%f) = %.4f", x, sum);

  return 0;

}

// Hope that addresses your questions.