Consider the function f(x) = 3 e-X. Answer the questions below. (a) Find the third order Taylor Polynomial P3(x) for f(x) centered at a = 0. (Type an expression involving x. Simplification is not required.) (b) Use your polynomial from part (a) to approximate the value of 3 e - 0.5 The approximate value is (Type an integer or decimal rounded to 4 decimal places as needed.) (c) Use the bound from Taylor's Remainder Theorem to find the maximum possible error (that is, find a bound on |Ral) in your approximation from part (b). Using M = (type an exact answer), the error bound according to Taylor's Remainder Theorem is IR3|S (type a decimal value rounded to 6 decimal p
Consider the function f(x) = 3 e-X. Answer the questions below. (a) Find the third order Taylor Polynomial P3(x) for f(x) centered at a = 0. (Type an expression involving x. Simplification is not required.) (b) Use your polynomial from part (a) to approximate the value of 3 e - 0.5 The approximate value is (Type an integer or decimal rounded to 4 decimal places as needed.) (c) Use the bound from Taylor's Remainder Theorem to find the maximum possible error (that is, find a bound on |Ral) in your approximation from part (b). Using M = (type an exact answer), the error bound according to Taylor's Remainder Theorem is IR3|S (type a decimal value rounded to 6 decimal p
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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Transcribed Image Text:Consider the function f(x) = 3 e -X. Answer the questions below.
(a) Find the third order Taylor Polynomial P3(x) for f(x) centered at a = 0.
(Type an expression involving x. Simplification is not required.)
(b) Use your polynomial from part (a) to approximate the value of 3 e -0.5
The approximate value is.
(Type an integer or decimal rounded to 4 decimal places as needed.)
(c) Use the bound from Taylor's Remainder Theorem to find the maximum possible error (that is, find a bound on IRl) in your approximation from part (b). Complete th
Using M = (type an exact answer), the error bound according to Taylor's Remainder Theorem is IR3|S (type a decimal value rounded to 6 decimal places as nee
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