work and write the cosine function's taylor expansion (N=10) in C++ and compare the with your version (see nartual exponent EXP() vs exp()). EQUATION ATTACHED.    EXAMPLE: #include #include using namespace std; // lazy technique // Factorial Recursion. // https://en.wikipedia.org/wiki/Factorial // write the factorial function as a loop (iteration) // This might seem trivial, but people have researched this // this topic. Sterling series approximation // https://en.wikipedia.org/wiki/Stirling_approximation int fact(int N) { if (N == 0) return 1; else return N * fact(N - 1); } // taylor series approximation for the // natural exponent 2.718... which is abbreviated as exp. double EXP(double x) { double sum = 0.0; for (int i = 0; i < 10; i++) sum += pow(x, i) / fact(i); return sum; } // dummy--aka place holder--functions. double SIN(double x) { return 1; } double COS(double x) { return 0; } int main() { std::cout << "e-World!\n"; for (double x = 0.0; x <= 1.0; x += .1) { cout << x << '\t' << EXP(x)<<'\t'<

work and write the cosine function's taylor expansion (N=10) in C++ and compare the <cmath> with your version (see nartual exponent EXP() vs exp()). EQUATION ATTACHED. 

EXAMPLE:

#include <iostream>

#include <cmath>

using namespace std; // lazy technique

// Factorial Recursion.

// https://en.wikipedia.org/wiki/Factorial

// write the factorial function as a loop (iteration)

// This might seem trivial, but people have researched this

// this topic. Sterling series approximation

// https://en.wikipedia.org/wiki/Stirling_approximation int fact(int N) { if (N == 0) return 1; else return N * fact(N - 1); }

// taylor series approximation for the

// natural exponent 2.718... which is abbreviated as exp.

double EXP(double x) { double sum = 0.0;

for (int i = 0; i < 10; i++)

sum += pow(x, i) / fact(i);

return sum; } // dummy--aka place holder--functions.

double SIN(double x) { return 1; }

double COS(double x) { return 0; }

int main() {

std::cout << "e-World!\n";

for (double x = 0.0; x <= 1.0; x += .1) {

cout << x << '\t' << EXP(x)<<'\t'<<exp(x) << endl;

}

}