28. Let f be a function that has derivatives of all orders for all real numbers, and let P3(x) be the third-degree Taylor polynomial for ƒ about x = 0. The Taylor series for f about x = 0 converges at x = 1, and 11 | ƒ(^) (x)| ≤ ,₁² + 1 for 1 ≤ n ≤ 4 and all values of x. Of the following, which is the smallest value of k fo which the Lagrange error bound guarantees that |ƒ(1) - P3(1)| ≤ k ? (A) // (B) (C) (0) (D) A/W U/A VITA V/A 1 5 4! 11/10 5 3! 3 1 4 4!
28. Let f be a function that has derivatives of all orders for all real numbers, and let P3(x) be the third-degree Taylor polynomial for ƒ about x = 0. The Taylor series for f about x = 0 converges at x = 1, and 11 | ƒ(^) (x)| ≤ ,₁² + 1 for 1 ≤ n ≤ 4 and all values of x. Of the following, which is the smallest value of k fo which the Lagrange error bound guarantees that |ƒ(1) - P3(1)| ≤ k ? (A) // (B) (C) (0) (D) A/W U/A VITA V/A 1 5 4! 11/10 5 3! 3 1 4 4!
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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28. Let f be a function that has derivatives of all orders for all real numbers, and let P3(x) be the third-degree
Taylor polynomial for ƒ about x = 0. The Taylor series for f about x = 0 converges at x = 1, and
|ƒ(")(x)| ≤ „² for 1 ≤ n ≤ 4 and all values of x. Of the following, which is the smallest value of k for
"+1
which the Lagrange error bound guarantees that |ƒ(1) – P3(1)| ≤ k ?
(A)
5 4!
4 1
.
5 3!
3 1
(D)
.
4 4!
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4 3!
(B)
(C)
€
139, Vietnam
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