1 5) a) Using the identity Σ 1- X x" derive a power series representation for the function n=0 1 f(x)= 1+ x10 1 b) Using the identity y2n derive a power series representation for the function 1+ x? n=0 f(x)= tan (2x) .

(a) Find a power series representation for  f(y) =(y^2)/(b+y^3), b >0. use Σ notation, with nothing in front of (or outside of) the Σ, with only one factor for each variable or constant, and no fractions within fractions.   (b) State the radius of convergence of your power series

7. (a) Find the Taylor series of the function f(x) = x³ – 2.x + 4 at x = 2 - (b) Find the Maclaurin series of the function f(x) = e

1. Given the function f(x) = ln x a) Find the Taylor polynomial p5 for f(x) = ln x at a = 3. b) Write the power series using summation notation.