Let f(x)= cos x and derive its Maclaurin Series, and find its interval of convergence.

Use the power series 1 + x x n-0 to find a power series for the function, centered at 0. f(x) = arctan 9x (x) = E Determine the interval of convergence. (Enter your answer using interval notation.)

Find a power series representation for the function. f(x) = x6 tan-1(x³) (x) = S n = 0 Determine the radius of convergence, R. R =

Find the Maclaurin series forf(x) = 1/(6-x-x2)and determine its radius of convergence. You must find an explicit expression for the coefficients in the power series.