MAC 2311C Lecture 32: 11.9 Representations of functions as power series

Use the established power series representations for functions to find a power series representation for d tan() dx 4. (change to a power series first - do not use the quotient rule!): (5 points)

6. + 1/2 points ! Previous Answers SCalcET8 11.9.016 Find a power series representation for the function. f x) = x4 tan-1(x3) f(x) = 2nl-1 n=0 L Determine the radius of convergence, R. R=1

☠2) Find power series representations for the following functions and determine the interval of convergence 2r3 b) f(x) =-1 a) f(x) = +2 Hint: It might be useful to perform algebraic manipulations of these functions to transform them into know series expansions, such as the geometric series.