For the following questions, you may use either the direct method (i.e. definition of Maclaurin se- ries) or start from a known series such e*, sin x, arctan x, and ln(1 +x). geometric series, binomial series, or the Maclaurin series for (a) If f(x) = (1 + x³)30, find f(58)(0). (b) If g(x) = sin(x³), find g(15)(0). (c) Suppose you know that f(x) is a function such that the Taylor series of f centered at 4 converges to f (x) for all x in the interval of convergence. If (-1)"n! (а-1)"(п+ 1) f(^(a) = show that the fifth degree Taylor polynomial centered at 4 approximates f(5) with error less than 0.0002.
For the following questions, you may use either the direct method (i.e. definition of Maclaurin se- ries) or start from a known series such e*, sin x, arctan x, and ln(1 +x). geometric series, binomial series, or the Maclaurin series for (a) If f(x) = (1 + x³)30, find f(58)(0). (b) If g(x) = sin(x³), find g(15)(0). (c) Suppose you know that f(x) is a function such that the Taylor series of f centered at 4 converges to f (x) for all x in the interval of convergence. If (-1)"n! (а-1)"(п+ 1) f(^(a) = show that the fifth degree Taylor polynomial centered at 4 approximates f(5) with error less than 0.0002.
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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Can I please get the answers for b and c?
Transcribed Image Text:For the following questions, you may use either the direct method (i.e. definition of Maclaurin se-
ries) or start from a known series such as geometric series, binomial series, or the Maclaurin series for
e*, sin x, arctan x, and ln(1 +x).
(a) If f(x) = (1+x³)30, find f(58)(0).
(b) If g(x) = sin(x³), find g(15)(0).
(c) Suppose you know that f (x) is a function such that the Taylor series of f centered at 4 converges to
f (x) for all x in the interval of convergence. If
(-1)"n!
flm)(a) =
(а-1)"(п + 1)"
show that the fifth degree Taylor polynomial centered at 4 approximates f(5) with error less than
0.0002.
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