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.
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.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:Show that if n is a natural number and a, B are real numbers with 8 > 0 then there exists
a real function f with derivatives of all orders such that: (i) |f(k)(x)| < ß for k e {0,1,..,n – 1}
and r € (-00, 00); (ii) f(k) (0) = 0 for k E {0, 1, ..., n – 1}; (iii) f(m)(0) = a.
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