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Use the complete Horner's algorithm to write the Taylor series for the following function at the point indicated. ³2x² + 4x-1 at 2 375-27³ +5²-1 at -1

Use the complete Horner's algorithm to write the Taylor series for the following function at the point indicated. ³2x² + 4x-1 at 2 375-27³ +5²-1 at -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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**Using Complete Horner’s Algorithm for Taylor Series Expansion** Apply Horner's algorithm to express the Taylor series for the following functions at the specified points: 1. \( x^3 - 2x^2 + 4x - 1 \) at \( x = 2 \) 2. \( 3x^5 - 2x^3 + 5x^2 - 1 \) at \( x = -1 \) **Explanation:** To write the Taylor series using Horner’s algorithm, begin by organizing the polynomial into nested form for efficient computation. Horner's method minimizes the number of multiplications required to evaluate the polynomial and its derivatives, which is particularly useful for calculating Taylor series expansions at a given point.
Transcribed Image Text:**Using Complete Horner’s Algorithm for Taylor Series Expansion** Apply Horner's algorithm to express the Taylor series for the following functions at the specified points: 1. \( x^3 - 2x^2 + 4x - 1 \) at \( x = 2 \) 2. \( 3x^5 - 2x^3 + 5x^2 - 1 \) at \( x = -1 \) **Explanation:** To write the Taylor series using Horner’s algorithm, begin by organizing the polynomial into nested form for efficient computation. Horner's method minimizes the number of multiplications required to evaluate the polynomial and its derivatives, which is particularly useful for calculating Taylor series expansions at a given point.
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