Question 9 A function (r) satisfies (1 – 12)}"(*) – 2f'(x) + f(x) = 0. (a) If n is a positive integer, what is the value

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Question 9 A Function R Satisfies 1 12 2f X F X 0 A If N Is A Positive Integer What Is The Value 1 (20.05 KiB) Viewed 22 times

Question 9 A function (r) satisfies (1 – 12)}"(*) – 2f'(x) + f(x) = 0. (a) If n is a positive integer, what is the value of K in the following (6 marks) (1 - x)/(1+2)(x) = x(2n + 1)f(n+1)(x) + K/")(x) = 0. ! k!(n-k)! (b) Given that so = 1 and f'() = 0 find the values of f"0), 130, () and fo). Hence, determine the Maclaurin series of f(*) as far as the terms in r". (4 marks) Hint: (89)"}(x) = ¿ (*);"(a): gyu-Y(), where (3) (%) - n!