Let Assume that f has a continuous derivative on a, b. Show tha p(x) such that |f(r) – p(x)| < e and |f' (x) – p (x)| < e for all r e (a) Show f is defined for r > 0. (b) Show that f is continuous on (0, 0). (c) Is f differentiable on (0, 0)?

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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Let Assume that f has a continuous derivative on [a, b]. Show that there exists a polynomial
p(x) such that |f(x) – p(T)| < e and |f'(x) – p'(x)| < e for all æ € [a, b].
(a) Show f is defined for r > 0.
(b) Show that ƒ is continuous on (0, o0).
(c) Is f differentiable on (0, o0)?
Transcribed Image Text:Let Assume that f has a continuous derivative on [a, b]. Show that there exists a polynomial p(x) such that |f(x) – p(T)| < e and |f'(x) – p'(x)| < e for all æ € [a, b]. (a) Show f is defined for r > 0. (b) Show that ƒ is continuous on (0, o0). (c) Is f differentiable on (0, o0)?
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