In (11 1)! DO Question 4. The series 2 is the Taylor series generated by f (I) = :56" n=l at a: = 0. By using this fact; ((1) Write the Taylor polynomial generated by f at :c = O. (b) Write a polynomial of order 3 which provides the best polynomial approximation off around :5 = 0. (c) Investigate the limit of the remainder (error term) lim R" (3:). n'DO (d) Does the given Taylor series converges to f for every real value of 2:? Why