derivatives of all orders exist in an open interval including x=1. Which of the following results will be obtained if we calculate an approximate value for f(1,3) with the help of the 2nd order Taylor polynomial centered at x=1 together with the appropriate values in the table.

derivatives of all orders exist in an open interval including x=1. Which of the following results will be obtained if we calculate an approximate value for f(1,3) with the help of the 2nd order Taylor polynomial centered at x=1 together with the appropriate values in the table.

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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Question

The value of the function f(x) and some order derivatives at the point
x=1 are given in the following table where f(x) is a function whose
derivatives of all orders exist in an open interval including x=1. Which of
the following results will be obtained if we calculate an approximate value
for f(1,3) with the help of the 2nd order Taylor polynomial centered at
x=1 together with the appropriate values in the table.
f(x) | f'(x)| f"(x) | f"(x) | f(4)(x)
1
1
-1
2
-6
24
(a) 0,79
(b) 0,78
(c) 0,76
(d) 0,75
(e) 0,74

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