What is the advantage of using maclaurin expansion of functions like tan(x) over using the functions themselves?

332 Views Asked by At

For example, using the maclaurin series of tan(x) instead of tan(x) has the disadvantage that the series and the function agree only for a very small neighbourhood around 0 and for that very small value of x, we can rather use the trigonometric limit, {limit (x ->0)} tan(x) = 0 What is the point of using the expansion then? How do we find the exact domain where these functions match with their respective maclaurin expansions?