1. The problem states that Taylor series is the elder brother of Maclaurin series. 2. Let's clarify the relationship: A Taylor series is a representation of a function as an infinite sum of terms calculated from the values of its derivatives at a single point $a$. 3. The formula for the Taylor series of a function $f(x)$ about the point $a$ is: $$f(x) = \sum_{n=0}^\infty \frac{f^{(n)}(a)}{n!} (x - a)^n$$ 4. The Maclaurin series is a special case of the Taylor series where the expansion point $a=0$: $$f(x) = \sum_{n=0}^\infty \frac{f^{(n)}(0)}{n!} x^n$$ 5. So, the Maclaurin series is essentially the Taylor series centered at zero. 6. In simple terms, the Taylor series generalizes the Maclaurin series by allowing expansion around any point $a$, not just zero. 7. Therefore, calling Taylor series the "elder brother" of Maclaurin series is a metaphor indicating that Maclaurin series is a specific, simpler case of the more general Taylor series.