(Solved): show all work please 6. Use your knowledge of power series to answer the following. (a) Find a power ...

6. Use your knowledge of power series to answer the following. (a) Find a power scries representation for \( f(x)=\frac{4 x}{4+x^{4}} \) (b) The function \( F(x)=\arctan \left(\frac{x^{2}}{2}\right) \) has derivative \( F^{\prime}(x)=f(x) \), where \( f(x) \) is the function in part (a). Find a power series representation for \( F(x) \).