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The value of the function f(x) is known at three points f(0) = 1, f (1) = 2,f(3) = -1. (a) Write down the first three terms of the Taylor series f(x) about x = 1. (b) Use the Taylor series from part (a) to express f(0) and f(3). (c) Determine f'(1) and the second derivatives f"(1).

The value of the function f(x) is known at three points f(0) = 1, f (1) = 2,f(3) = -1. (a) Write down the first three terms of the Taylor series f(x) about x = 1. (b) Use the Taylor series from part (a) to express f(0) and f(3). (c) Determine f'(1) and the second derivatives f"(1).

Advanced Engineering Mathematics
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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The value of the function f(x) is known at three points f(0) = 1, f(1) = 2 , f (3) = -1. (a) Write down the first three terms of the Taylor series f(x) about x = 1. (b) Use the Taylor series from part (a) to express f (0) and f(3). (c) Determine f'(1) and the second derivatives f"(1).
Transcribed Image Text:The value of the function f(x) is known at three points f(0) = 1, f(1) = 2 , f (3) = -1. (a) Write down the first three terms of the Taylor series f(x) about x = 1. (b) Use the Taylor series from part (a) to express f (0) and f(3). (c) Determine f'(1) and the second derivatives f"(1).
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