(a) If a function f has nth Taylor polynomial pn(x) aboutx = x0, then the nth remainder
Chapter 9, Problem 5(choose chapter or problem)
(a) If a function \(f\) has \(n\)th Taylor polynomial \(p_{n}(x)\) about \(x=x_{0}\), then the \(n\)th remainder \(R_{n}(x)\) is defined by \(R_{n}(x)\) = ________.
(b) Suppose that a function \(f\) can be differentiated five times on an interval containing \(x_{0}=2\) and that \(\left|f^{(5)}(x)\right| \leq 20\) for all \(x\) in the interval. Then the fourth remainder satisfies \(\left|R_{4}(x)\right| \leq\) ________ for all \(x\) in the interval.
Equation Transcription:
Text Transcription:
f
n
p_n(x)
x = x_0
n
R_n(x)
R_n(x)
f
x_0 = 2
|f^(5) (x)| leq 20
x
|R_4(x)| leq
x
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