Show that if n is a natural number and a, ß are real numbers with 8 > 0 then there exists a real function f with derivatives of all orders such that: (i) \F®) (x)| < B for k e {0, 1, ...,n – 1} and z E (-00, 00); (ii) F(R (0) = 0 for k € {0, 1, .., n – 1}; (iii) f(»)(0) = a.

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