Problem 2 [25 pts] On Midterm 4, one of the problems dealt with Bessel functions, which arise in various engineering and physics applications. They are solutions to the differential equation 2 2 day dr2 + di dy + (2 2 - a2 ) y = 0, and it can be shown that there is no "nice" formula for them. When a = 1, it can be shown that the power series is JI(c) = (-1) * -2k+1 2k . k!(k + 1)!" is a solution to this equation. On your project, you should have shown that the open interval of convergence for this series was (-co, co) and hence, the higher order Taylor polynomials should provide better approximations than the lower order ones if we want to approximate Ji(1). Report your final answer to 6 decimal places. A. [3 pts] Use the third order Taylor polynomial for Ji(r) to approximate Ji (1). B. [12 pts] Explain why the alternating series remainder results can be used to find the maximum possible error made by this approximation, and calculate this maximum possible error to 6 places