(d) Find the error estimates |R3(0.5)| and |R3(-0.5)| given by the Taylor's remainder. N+(E) (N + 1)! (z-c)N+1, RN(2) =
(d) Find the error estimates |R3(0.5)| and |R3(-0.5)| given by the Taylor's remainder. N+(E) (N + 1)! (z-c)N+1, RN(2) =
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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Please solve only d part within 30-40 mins I'll give you multiple upvotes
Transcribed Image Text:(a) Find the third Taylor polynomial Pa(r) for the function f(z) = Va +1 about c = 0.
%3D
PN(z) = S(c) + f'()(r-e)+ (- c)² +.+
N)(e)
fin) (c) (-e)"
2!
N!
n!
(b) Approximate V0.5 and V1.5 using Pa(x).
(c) Compare your result with actual cube roots (as given by a calculator).
(d) Find the error estimates R3(0.5)| and |R(-0.5)| given by the Taylor's remainder.
N+(),
(N+1) ( - c)N+1,
RN(1) =
where { is between z and c.
(e) Compare the actual error with the error estimate.
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