(Solved): Find the Maclaurin series for \( f(x) \) using the definition of a Maclaurin series. [Assume that ...

Find the Maclaurin series for \( f(x) \) using the definition of a Maclaurin series. [Assume that \( f \) has a power series expansion. Do not show that \( R_{n}(x) \rightarrow 0 . \) ] \[ \begin{array}{c} f(x)=\sin \left(\frac{\pi x}{4}\right) \\ f(x)=\sum_{n=0}^{\infty}\left(\frac{(-1)^{n}(\pi)^{2 n+1}(x)^{2 n+1}}{4(2 n+1) !}\right) \\ \text { × } \end{array} \] Find the associated radius of convergence \( R \). \[ R= \] [-12 Points] SCALCET9 \( 11.10 .019 \) Find the Maclaurin series for \( f(x) \) using the definition of a Maclaurin series. [Assume that \( f \) has a power series expansion. Do not show that \( R_{n}(x) \rightarrow 0 . \) ] \[ \begin{array}{r} f(x)=5 \sinh (3 x) \\ f(x)=\sum_{n=0}^{\infty}( \end{array} \] Find the associated radius of convergence \( R \). \[ R= \]