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Consider the function f(x) = (1-x)² 1. Find the linear Taylor polynomial p₁(x) for f(x) centered at x = 0. 2. Find the quadratic Taylor polynomial p2(x) for f(x) centered at x = 0?

Consider the function f(x) = (1-x)² 1. Find the linear Taylor polynomial p₁(x) for f(x) centered at x = 0. 2. Find the quadratic Taylor polynomial p2(x) for f(x) centered at x = 0?

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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Please only question 1 and 2. Thank you !
1 Consider the function f(x) (1 − x)²* 1. Find the linear Taylor polynomial p₁(x) for f(x) centered at x = 0. 2. Find the quadratic Taylor polynomial p2(x) for f(x) centered at x = 0? 3. Find the Taylor polynomials Pp3 and p4 centered at x = 0. 4. Use p4(x) to approximate to 3 decimal places. 1 0.92 (What is the value of a needed in f(x)?) Round your answer
Transcribed Image Text:1 Consider the function f(x) (1 − x)²* 1. Find the linear Taylor polynomial p₁(x) for f(x) centered at x = 0. 2. Find the quadratic Taylor polynomial p2(x) for f(x) centered at x = 0? 3. Find the Taylor polynomials Pp3 and p4 centered at x = 0. 4. Use p4(x) to approximate to 3 decimal places. 1 0.92 (What is the value of a needed in f(x)?) Round your answer
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