. Let f(x) = tan(x). In the following we would like to calculate the erors. (a) First write down the approximate polynomial, ps(r), for the function f(x) and identify the Taylor coefficients, ao,, 03. Compute the relative error at x = π/4 if f(x) is approximated by p3(x) polynomial. Use the Lagrange reminder form to evaluate the upper bound of the error for some € [0, π/4]. (b) (c)
. Let f(x) = tan(x). In the following we would like to calculate the erors. (a) First write down the approximate polynomial, ps(r), for the function f(x) and identify the Taylor coefficients, ao,, 03. Compute the relative error at x = π/4 if f(x) is approximated by p3(x) polynomial. Use the Lagrange reminder form to evaluate the upper bound of the error for some € [0, π/4]. (b) (c)
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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Question
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Need 4(c)
![3.
Let f(x) =
sin(x) + x - 1. To evaluate f(x) near zero we need to compare f(x) to the Taylor
expansion of f(x) at x = 0. Evaluate the Taylor coefficients, ao, a1, a2, if we compare f(x) with degree two
polynomial near zero.
-
4. Let f(x) =tan(x). In the following we would like to calculate the erors.
(a)
First write down the approximate polynomial, p3(x), for the function f(x) and identify the Taylor
coefficients, ao,, 03.
Compute the relative error at x = π/4 if f(x) is approximated by p3(x) polynomial.
Use the Lagrange reminder form to evaluate the upper bound of the error for some § € [0, π/4].
(b)
(c)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F29714931-baa3-4a6c-b6e9-d913d8c26057%2F42f79bf0-6a94-4892-988b-4473709b4c12%2F3dq8fcm_processed.jpeg&w=3840&q=75)
Transcribed Image Text:3.
Let f(x) =
sin(x) + x - 1. To evaluate f(x) near zero we need to compare f(x) to the Taylor
expansion of f(x) at x = 0. Evaluate the Taylor coefficients, ao, a1, a2, if we compare f(x) with degree two
polynomial near zero.
-
4. Let f(x) =tan(x). In the following we would like to calculate the erors.
(a)
First write down the approximate polynomial, p3(x), for the function f(x) and identify the Taylor
coefficients, ao,, 03.
Compute the relative error at x = π/4 if f(x) is approximated by p3(x) polynomial.
Use the Lagrange reminder form to evaluate the upper bound of the error for some § € [0, π/4].
(b)
(c)
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