Homework Question Charles Sturt University - Question 1a: (2 points) For the alternating series (-1)n+1 =1 2n2 - 1 a) Use the sum of the first four terms of the series to estimate the infinite sum correct to 4 decimal places: b) Use the rule for alternating series to calculate the error bound on the estimate from the previous question to 4 decimal places: Question 1b: (7 points) The goal of this question is to estimate (1.5) 3/ using the first three terms of the Taylor series for the function f (x) = (1+2)3/5 a) On your working paper, calculate the derivatives f (x) and f"(x), and then evaluate the following: f(0) = f'(0) = f" (0) = b) The first three terms of the Taylor series are given by the expression f (x) = f(0) + f' (0) x + 1 102 + ... Using this expression and your values from above, enter the Taylor series 2! up to the term in ac2 : f (x) ~ c) Estimati.5)3/5 = (1 + 0.5)3/5 = f(0.5) using the first three terms of the Taylor series with x = 0.5 and enter the value correct to 4 decimal places: f (0.5) ~ d) Next we will use the remainder theorem to obtain an error bound on your estimate. Find the error bound using the formula bel and enter the value correct to 4 decimal places |R2(0.5) | 5 max f" ( 2) ( 0.5) 3 = 0