Please show your steps and detailed work

1. (10 marks total) Suppose (_1}nm 2n. f(e:)= : 2 n f 2 M 2 (n J is the Maclaurin series of the function f , and that it converges for all a: E R (not for marks: you should be able to show this). (a) (3 marks) What is the value of f(1000)(0)? Do not evaluate large factorials or powers in this expression. (b) (7 marks) Show that the function f solves the equation sz"($) + If'($) + 9621\" (II?) =