So I understand how to set up this series but I'm just confused on the last part so the question is find the maclaurin series for the following:
$$f(x) = 15x \cos \left( \frac{1}{14}x^2 \right)$$
so its easy to plug the values in the $\cos(x)$ formula for the maclaurin series, I just don't what to do with the 15 on the outside. I know that the $x$ goes and you just add 1 to the $x$ exponent but the 15 I don't know where to plug in. If anyone could help that would be great.
Best Answer
You can just use the series expansion: $$\cos u = 1 - \frac{u^2}{2!} + \frac{u^4}{4!} - \cdots$$ then substitute $u$ for $\frac{x^2}{14}$, and finally multiply everything for $15x$. Probably it's the easiest way. Ok?