Find the 3rd derivative using finite difference approach via the Taylor series

2(-1)* -(x + 2)*. Write down the first four terms of it, 32k+1 k=0 Question: Consider the power *series and find a rational function representation of it.

(-1)^n! 1) Suppose we know that f(n) (4) = and the Taylor series of f 3n (n+1) centered at 4 converges to f(x) for all x in the interval of convergence. Show that the fifth-degree Taylor polynomial approximates f(5) with error less than 0.0002.