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# Calculation of a function with the help of a Taylor series

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Real function can be represented by a series of Taylor, the radius of the convergence of which is determined by the position of the singular points of the function. Any final segment of the Taylor series is a polynomial, so it can be calculated using addition and multiplication operations.

The program calculates the `ln (1-x) `function. Help please remake calculations in the code for the `exp (x ^ 2 function `.

``````# include & lt; stdio.h & gt;
#Include & lt; stdlib.h & gt;
#Include & lt; math.h & gt;
// This Function Is Calculating The Power Of X
Double Powx (Double X, Int i)
{
Switch (I)
{
Case 0:
Return 1;
Case 1:
Return x;
Default:
RETURN X * POWX (X, I - 1);
}
}
// This Function Is Calculating The Value Of A Member of the Serie
Double Membvalcalc (Double X, Int i)
{
RETURN -1 * (POWX (X, I) / I);
}
INT MAIN ()
{
/ * ACC = accuracy; result = aproximated value; ET_Result = Contain Library Value;
AprDiff = Is The Difference Between Library's Value and The Result of this Program's Work * /
Double X, ACC, Result, Membval, Et_result, AprDiff, Achievedacc;
int i, j = 0,
n; // N - IS The Maximal Member of Serie In The Calculation
PrintF ("This Program Will Calculate Function LN (1-X). \ n");
Printf ("Please, Enter X Value Between -1.0 and 1.0 AS 'Double' Type:");
ScanF ("% LF", & amp; x);
// Area of â€‹â€‹Definition of this Function; IF X NOT Belong To This Area, The Program Will Be Closed
if ((X & LT; -0.9999999) || (X & GT; 0.9999999))
{
PrintF ("Error: X Must Be The Value Between -1 and 1. \ n");
Return -1;
}
Printf ("Please, Enter N Value As 'Integer' Type:");
Scanf ("% d", & amp; n);
Printf ("Enter Accuracy of Calculation AS 'Double' Type:");
Scanf ("% LF", & amp; ACC);
If (ACC & LT; 0)
{
PrintF ("Error: Accuracy Is Negative Number.");
Return -1;
}
RESULT = 0.0;
// This for Loop Is Calculating Each Member of The Serie and Increase The Result Variable by This Value
for (i = 1; i & lt; = n; i ++)
{
Membval = Membvalcalc (X, I);
j = i;
if ((Membval & gt; 0) & amp; & amp; (Membval & lt; = ACC))
{
j = i - 1;
Break;
}
ELSE If ((Membval & LT; 0) & amp; & amp; ((Membval * -1) & lt; = ACC))
{
j = i - 1;
Break;
}
ELSE.
{
Result + = Membval;
}
}
ET_RESULT = log (1 - x);
if (result & gt; = 0) & amp; & amp; (et_result & gt; = 0))
{
APRDIFF = RESULT - ET_RESULT;
}
ELSE if ((Result & lt; 0) & amp; & amp; (et_result & lt; 0))
{
APRDIFF = (result * -1) - (et_result * -1);
}
ELSE.
{
APRDIFF = RESULT + ET_RESULT;
}
Achievedacc = Membvalcalc (x, j);
if (APRDIFF & LT; 0)
{
APRDIFF * = -1;
}
if (Achievedacc & lt; 0)
{
Achievedacc * = -1;
}
PrintF ("Total Quantity of Calculated Members of the Serie:% D \ N", j);
Printf ("The Achieved Accuracy of Calculation IS% F \ N", Achievedacc);
PrintF ("The result log (1-x) is:% LF \ N", Result);
Printf ("Using the Math.h Library We Could Get The Result Log =% LF \ N"
et_result);
Printf ("The Difference Between Calculated Approximation and Library's Value:% LF",
APRDIFF);
Return 0;
}
``````

in general, insert where you need – here is a function that believes `exp (x ^ 2) `with the accuracy `EPS `decomposition in a Taylor series:

``````double expx2 (double x, double eps)
{
Double Sum = 1.0, Term = 1.0;
x = x * x;
For (int n = 1; Term & gt; eps; ++ n)
{
SUM + = TERM * = X / N;
}
Return Sum;
}
``````

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