# Libraries¶

## Find the libraries (0.5p)¶

We are writing a library to calculate how many terms do we need in a Taylor series so the error is close to 0. We are using different libraries, but for some reasons they were removed from our file.

Fix the code below so that it works. In practise you just need to find the missing libraries and include them.

```
// missing include-files
double perm_product(int n) {
if (n == 0) return 1;
double result = 1;
for (int i = 1; i <= n; i++) {
result *= i;
}
return result;
}
// Function to calculate Taylor series for e^x
double taylor_exp(double x, int terms) {
double sum = 1.0;
for (int n = 1; n <= terms; n++) {
sum += pow(x, n) / perm_product(n);
}
return sum;
}
int main() {
uint8_t i = 1;
srand(time(NULL));
// Choose a random value for x in the Taylor series
double x = ((double)rand() / RAND_MAX) * 10.0; // Random x between 0 and 10
printf("Calculating e^%f using Taylor series:\n\n", x);
// Random value for j between 0 and SCHAR_MAX
uint8_t j = rand() % (SCHAR_MAX + 1);
printf("Number of terms for the Taylor series: %d (random between 0 and SCHAR_MAX)\n", j);
// Start timing after j is calculated
clock_t start, end;
start = clock();
// Calculate the Taylor series with up to j terms
do {
// Calculate the Taylor series with i terms
double taylor_result = taylor_exp(x, i);
// Exact value of e^x
double exact_result = exp(x);
// Print the number of terms and the comparison
printf("Using %d term(s): Taylor series = %f, Exact = %f, Difference = %f\n",
i, taylor_result, exact_result, fabs(exact_result - taylor_result));
i++;
} while (i <= j);
// End timing
end = clock();
printf("\nFinal number of terms: %d\n", j);
printf("Loop took %f seconds to run\n", (double)(end - start) / CLOCKS_PER_SEC);
return 0;
}
```

Note that no errors nor warnings are accepted in your answer.

**Hint**: Remember when testing your code, you must include -lm flag in gcc to be sure math library is used.

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