Use Python for the programs asked in (1), (2), and (3) For each question below,

Question

Use Python for the programs asked in (1), (2), and (3)

For each question below, write a small Python (or C, or C++, ...) function. The arguments of the trigonometric functions are angles expressed in radians. How could we compute (cos(x) - 1)/x^2 for values of x that are very close to 0? Use the Taylor series of cos(x) near 0. Compare the Taylor series method with the direct evaluation of the formula (cos(x) - 1)/x^2 (in Python, or C, etc.), when |x| is small. Use the values 10^-6, 10^-10, 10^-16, 0 for x. Similarly, how could we compute sin(x)/x for values of x that are very close to 0? Again, use the Taylor formula. Suppose we have a function s(.) that computes s(x) = sin(x) for 0 lessthanorequalto x lessthanorequalto pi: s(x) is undefined when x

Explanation / Answer

#include #include using namespace std; double fact (int); double eps; double PI=3.141592654; double fact (int num){ if (num==0 || num==1) return 1; else return num*fact(num-1); } int main(){ double deg; double rad; double term=0.0; double sum=0.0; double cosine=0.0; int i=1; coutdeg; rad=(PI/180)*deg; cout

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