Question: For questions below, write small Python (or C, or C++, ...) functions. The functions should have no side-effects; i.e., the input is the argument of
For questions below, write small Python (or C, or C++, ...) functions. The functions should have no side-effects; i.e., the input is the argument of the function, and the output is the return value (in particular, the functions should not contain print commands). The arguments of the trigonometric functions are angles expressed in radians.
1 How could we compute (cos(x) 1)/x2 with good precision, for values of x that are very close to 0? Use the Taylor formula of cos(x) near 0.
2 Compare the Taylor formula method with the direct evaluation of the formula (cos(x) 1)/x2 (in Python, or C, etc.), when |x| is small: use the values 10-6, 10-10, 10-16, 0 for x.
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