for 1 a instead of using the power series representations of sin(x), cos(x) etc, you need to use the given power series representation of f(x). I just need b and c A wont be needed 1.Consider the function2kf(x) =k=0defined for all x E R. (The series converges for all x E R.)f (x) — 1 — 2х — х?(a)Compute lim(Note: 0° = 1.)8x3(b)Find f(n) (0) for all n > 0.(c)Find a power series representation for f(n) (x) for all n >0 and all x E R.

Here we find the n'th derivative of x^i.

Answered: Find f(n) (0) for all n > 0.

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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for 1 a instead of using the power series representations of sin(x), cos(x) etc, you need to use the given power series representation of f(x). I just need b and c A wont be needed

1.
Consider the function
2k
f(x) =
k=0
defined for all x E R. (The series converges for all x E R.)
f (x) — 1 — 2х — х?
(a)
Compute lim
(Note: 0° = 1.)
8x3
(b)
Find f(n) (0) for all n > 0.
(c)
Find a power series representation for f(n) (x) for all n >0 and all x E R.

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