Question 9 A function f(x) satisfies (1 - x)}"(.) – xf'(x) + f(x) = 0. (a) If n is a positive integer, what is the value

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Question 9 A Function F X Satisfies 1 X Xf X F X 0 A If N Is A Positive Integer What Is The Value 1 (22.02 KiB) Viewed 24 times

Question 9 A function f(x) satisfies (1 - x)}"(.) – xf'(x) + f(x) = 0. (a) If n is a positive integer, what is the value of K in the following (1 - 2)f(n+2)(0) – (2n + 1) g(n+1)(x) + KfW (r) = 0. (6 marks) Hint: (19)"} (x) = Ï (3) s-> (a) : genky(), where n! k!(n-k)! (b) Given that f(0) = 1 and f'(0) O find the values of f"0), f), () and (6)(0) Hence, determine the Maclaurin series of f(x) as far as the terms in 2 (4 marks)