4 The function f(x) (1+4)² is represented as a power series: Find the first few coefficients in the power series. CO = C1 = C2 = C3 = C4 = Find the radius of convergence R of the series. R = ∞ f(x) = Σ enan n=0

1 (2 + x)(10 − x) - a. Find the Taylor series for f(x) centered at c = 14. Consider the function f(x) = = f(x) = Σ n=0 F b. Find the interval of convergence for the series found in Part a. Interval of convergence: ->

3. elemfe Consider the function f(x) = 2. (a) Find the Taylor series of f(x) at a = 5 using the definition of a Taylor series. (b) Find the radius of convergence of this power series. 1

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 =