(Solved): Find the Maclaurin series for \( f(x)=\cos (9 x) \) using the definition of a Maclaurin series: \[ ...

Find the Maclaurin series for \( f(x)=\cos (9 x) \) using the definition of a Maclaurin series: \[ \begin{array}{ll} f(x)= & , f(0)= \\ f^{\prime}(x)= & , f^{\prime}(0)= \\ f^{\prime \prime}(x)= & , f^{\prime \prime}(0)= \\ f^{(3)}(x)= & , f^{(3)}(0)= \\ \cos (9 x)= & , \\ x+\quad & x^{2}+ \end{array} \]