Use f(x) = -1 + ∫²ˣ₀ g(t) dt and the values below to answer the following questions.
g(0) = 1/4; g'(0) = -1/8; g"(0) = 3/32; g""(0) = -3/32
Part A: Create a polynomial approximation P₄(x) of the Taylor series generated by f(x) at x = 0.
Part B: Find the general term Pₙ(x) of the series in part a (assuming the pattern continues)
Part C: What is the interval of convergence of the general term in part b?
Part D: Using the information from the previous parts, show that |P₄(1/3) - f(1/3) | < 1/5000.
Part E: Using the general term, Pₙ(x) , you found in part b, determine if Рₙ(1/3) is absolutely or conditionally convergent. What is the value of |Р(1/3) | ? Show your work that leads to your conclusion.