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# please please find the values ​​of the SINX / X function using the Taylor series

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Find the values ​​of the SINX / X function using a series of Taylor on the range from Hnacht to the Clacon of the DX interval and accuracy. I wrote a function but after the second iteration value is not correct. I write in C++ Builder, below code:

``````{
Long Double XS, XE, DX, E, Y;
XS = STRTOFLOAT (EDIT1 - & GT; text);
XE = STRTOFLOAT (EDIT2 - & GT; TEXT);
DX = STRTOFLOAT (EDIT3 - & GT; TEXT);
E = STRTOFLOAT (EDIT4 - & GT; text) ;;
Memo1- & gt; lines- & gt; append ("f \ tx \ tn");
For (long double x = xs; x & lt; xe + dx / 2; x + = dx) {
int n = 0;
LONG DOUBLE AN = X;
y = 0;
While (Fabs (AN) & GT; E) {
y + = an;
N ++;
AN * = ((POW (-1, N)) * POW (X, 2 * N)) / FACT (2 * N + 1);
}
Memo1- & GT; Lines- & GT; Append (Floattostrf (y, fffixed, 10, 2) + "\ t" + Floattostrf (x, fffixed, 10, 2)
+ "\ t" + inttostr (n));
}
}
// ---------------------------------------------------- ---------------------------
LONG DOUBLE FACT (INT N)
{
if (n & lt; 0)
Return 0;
if (n == 0)
Return 1;
ELSE.
RETURN N * FACT (N - 1);
}
``````

In general, you have a mistake that if you want to search for `sin (x) / x `, then the Taylor formula will look like this:

``````sin (x) / x = 1 - x ^ 2/3! + X ^ 5/5! + ... + (-1) ^ n-1 * x ^ (2n - 2) / (2n - 1)!
``````

That is, you need to multiply not on `x ^ (2n) `, and on `x ^ (2n - 2) `.

Also not better to calculate the factorial and degree, and not every time on a new one?

Here is an example code if you do in the console:

``````void functionlor (Float Xstart, Float Xfinish, Float XStep, Float EPS) {
Long double FACT = 1;
LONG DOUBLE POW_X = 0;
Long long int c = 0;
INT SIGN = 1;
long double x = xstart;
LONG DOUBLE TEMP;
LONG DOUBLE SINX_X;
LONG DOUBLE AN = 0;
While (x + xstep & lt; = xfinish) {
FACT = 1;
POW_X = 1;
SIGN = 1;
C = 1;
sinx_x = sin (x) / x;
temp = 0;
do {
AN = (SIGN * POW_X) / FACT;
TEMP + = AN;
SIGN * = -1;
FACT = FACT * (C + 1) * (C + 2);
C + = 2;
POW_X * = X * X;
} While (/ * Fabs (AN) & GT; EPS * / SINX_X & lt; = temp - eps || sinx_x & gt; = temp + eps);
COUT & LT; & LT; TEMP & LT; & LT; "" & lt; & lt; x & lt; & lt; Endl;
x + = xstep;
}
}
``````

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