f(x) = 1+x+x² + x³+x²+x5. Find T3(x), the Taylor polynomial of f at x = 0 with degree 3 by using the definition of Taylor polynomials. Note that no partial mark will be given if the answer does not show work of using the definition of Taylor polynomials. Find the remainder R3(x) = f(x) — T3(x). Find the maximum value of ƒ(4) (x) on the interval |x| ≤ 0.1. Tuatifu that Torlon'a incanolity holda t for D. (0 ult from

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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Let f(x) = 1+x+x² + x³ + x¹+x5.
Find T3(x), the Taylor polynomial of ƒ at x = 0 with degree 3 by using the
definition of Taylor polynomials. Note that no partial mark will be given if the answer
does not show work of using the definition of Taylor polynomials.
Find the remainder R3(x) = f(x) — T3(x).
Find the maximum value of ƒ(4)(x) on the interval |x| ≤ 0.1.
Justify that Taylor's inequality holds true for R3(0.1) using your result from
the previous question.
1.
2.
3.
4.
Transcribed Image Text:Let f(x) = 1+x+x² + x³ + x¹+x5. Find T3(x), the Taylor polynomial of ƒ at x = 0 with degree 3 by using the definition of Taylor polynomials. Note that no partial mark will be given if the answer does not show work of using the definition of Taylor polynomials. Find the remainder R3(x) = f(x) — T3(x). Find the maximum value of ƒ(4)(x) on the interval |x| ≤ 0.1. Justify that Taylor's inequality holds true for R3(0.1) using your result from the previous question. 1. 2. 3. 4.
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